the same circuit, the mark made on the chronograph-paper, instead of being a straight line, will be broken at regular intervals as shown at a.
| aaaabaabaa |
| ____/\____/\____/\____/\__/\___/\____/\___/\___/\____/\____ |
By means of a little instrument called, a break-circuit key, in the hands of the observer, and included in the same circuit, the electric current may be interrupted, causing the pen to make a similar mark as shown at b, on the occurrence of any event, such as the passage of a star across the wires of the telescope.
With a finely-divided scale the position of this arbitrary mark, with reference to the nearest second mark, may be accurately established, and the exact time accurately ascertained to within 1⁄20 of a second.
By means of these instruments, the error of the chronometer is found at each station with great accuracy, and, the times shown by the faces of the chronometers being compared by telegraph, the difference of time and corresponding difference of longitude are readily deduced.
The time occupied by an electric impulse to traverse the wire from one station to another, and act upon the telegraph-instruments, though generally very small, is too great to be neglected, but is easily ascertained and allowed for.
Suppose a to be a station, one degree of longitude east of another station b, and that at each station there is a clock exactly regulated to the time of its own place, in which case the clock at a will be, of course, four minutes faster than the clock at b. Let us also suppose that a signal takes a quarter of a second to pass over the telegraph-wire connecting the two stations.
| Then if the observer at a sends a signal at exactly noon, by his clock,to 'b | 12h | 0m | 0s |
| It will be received at b at | 11h | 56m | 0s.25 |
| Showing apparently a difference of time of | 3m | 59s.75 | |
| Then if the observer at b sends a signal at noon by his clock | 12h | 0m | 0s |
| It will be received at a at | 12h | 4m | 0s.25 |
| Showing an apparent difference of time of | 4m | 0s.25 |
One-half the sum of these differences is 4, which is exactly the difference of time and of longitude; and one-half of their difference is 0.25, which is exactly the time taken by the electric impulse to traverse the wire and telegraph instruments. This is technically called the "wave and armature time."
The error of each chronometer being ascertained by observations of stars at each station, and the difference of the chronometers being in this way shown by the exchange of signals, the difference of the local times, which is the difference of longitude of the two stations, is easily deduced.
Some English astronomers have objected that, where the line is, as
