But experience has shown that no clock, however fine its mechanism, will run without change of error; so that, although for a particular instant the error of a clock is known by astronomical observation, it is by no means certain what will be its error for any subsequent instant. Its error for this instant can be determined with precision only by another observation. An approximation to its error al any instant can, however, be obtained by simple calculation, based upon two assumptions: first, that the change in error between the last two (or any previous two) observations was uniformly distributed over the interval of time between those observations, thus making it possible to determine a rate of change; second, that the rate of change in error since the last observation has been uniformly the same as during the previous interval. The reliability of this approximation is evidently entirely dependent upon an empirical knowledge of the clock. Cloudy weather sometimes makes this method the only resource.
In order that a clock should be used as an indicator of time, it is not enough that its error at every instant should be known; its error must be continually corrected so that its face-reading shall always indicate true time. And, in order that a clock should be used as a distributor of time, it must be provided with apparatus, distinct from the mechanism which keeps the time and in no way interfering with it, which is capable of sending time to other clocks. The methods and instruments in use in Paris for the accomplishment of these two objects will be described in this paper.
At the Paris Observatory a very fine standard clock or astronomical regulator is kept running on correct mean time by transit observations, being provided with the most approved self-compensating