is this: suppose that the detached pendulum is going slower than the clock pendulum; and suppose that 712 minutes elapse between two agreements of motion of the pendulum; then this shows that while the clock has gone 712 minutes, or while its pendulum has made 450 vibrations, the detached pendulum has made only 448 vibrations. Now, the clock is going day and night, and by means of observation with the transit instrument, you can find how many hours, minutes, and seconds, the clock hands pass over in one day, or how many vibrations the clock pendulum makes in one day. Then, as the detached pendulum makes 448 vibrations for every 450 made by the clock pendulum, you find at once how many vibrations the detached pendulum makes in 24 hours.
Some corrections for the effect of temperature in altering the length of the pendulum, and for other circumstances, are necessary; but I cannot enter upon the details of these at present. The method which I have described is exceedingly delicate. There is no difficulty in ascertaining by it the number of vibrations which the detached pendulum will make in a day, with no greater error than one-tenth of a vibration, or with an error not exceeding one eight-hundred-thousandth part of the whole.
This same pendulum is then carried to different parts of the earth, and is observed at every place in the same manner and with the same accuracy. The most important of our modern expeditions were those conducted by Colonel Sabine and Captain Foster. Each of these officers was entrusted by the Government with a ship, for the purpose of going to different parts of the earth, in order to observe the same pendulums at different places. Colonel Sabine went as
