THE RELATIVE FORCE OF GRAVITT AT KEW AND GREENWICH. 
541 
the vibrating pendulum less the tail-piece, which was fixed inside the receiver. In the 
Indian operations, the air was always exhausted to the lowest pressure attainable, and 
the vibration-number obtained at that pressure was reduced to the vacuum by special 
corrections, which will be afterwards described. At first the receiver was found to 
leak slightly, the pressure rising about an inch in the course of a day’s swings ; but 
eventually this leakage was traced to the two stuffing boxes, through which one 
rod passes for lowering the knife-edge on, or raising it off, the agate planes, and 
another rod for setting the pendulum in motion ; the leaks were stopped by fitting 
cups round the necks of the rods, and keeping them filled with oil. When the 
apparatus came into Colonel IIerschel’s hands much leakage was met with at the 
lower pressures. He continued to use the receiver, but he did not attempt to obtain 
low pressures, and he abandoned the reduction to the vacuum ; his pressures ranged 
between 26 and 28 inches, and his observations were reduced to an adopted standard 
pressure of 26 inches, with the temperature of the air at 32° F. The same procedure 
was adopted wFen the pendulums were swung by the officers of the United States’ 
Coast and Geodetic Survey. But wdien the apparatus was returned to England, the 
receiver was repaired and made thoroughly air-tight before the revision ary swings at 
Kew and Greenwdch were commenced ; then half the swings at each place were taken 
under a pressure of about 2 inches, and the other half at about 27 inches ; the results 
were reduced to a vacuum in both cases, by the same formula, which will be given 
hereafter. 
For each invariable pendulum the vibration-number is determined by swinging it in 
front of the pendulum of a clock and observing the times of the first and last coinci¬ 
dences of the two pendulums, at the beginning-and end of a set of swings; also the 
time of a coincidence immediately following the first, in order to get an approximate 
value of the interval between successive coincidences ; thus the number of swings made 
by the invariable pendulum during a given amount of clock time, is ascertained 
by observation, and from it the number of swings in 24 hours is calculated, after 
making due allowance for clock rate, arc of vibration, temperature, and pressure. The 
clock employed in the Indian and subsequent operations was one by Shelton, wdiich 
had been used for the same purpose by Sabine. The invariable pendulums make 200 
to 300 vibrations daily less than the pendulum of a clock regulated to solar time, and 
about twice that number to siderial time. 
For the observations of coincidence, in the Indian operations, a circidar disc of white 
metal was mounted on the bob of the clock pendulum, and an image of it, made very 
slightly less in diameter than the breadth of the tail-piece of the invariable pendulum, 
was produced, by an intermediate lens, in the plane of the tail-piece. The imago 
would disappear for a moment and then reappear behind the tail-piece at every 
apparent conjunction of the two pendulums ; and these conjunctions occur when both 
pendulums are swinging in the same direction, the intermediate conjunctions, with the 
swings in opposite directions, being unobservable. The exact moment of coincidence 
