Before the invention of the telegraph various methods more or less accurate in their results were employed, and are still in use where the telegraph is not available. The one most used and giving the best results was that in which a number of chronometers were transported back and forth between two places the difference of whose longitudes was required. "For," as the author quoted above says, "the determination of an absolute longitude from the first meridian or of a difference of longitude in general, resolves itself into the determination of the difference of the time reckoned at the two meridians at the same absolute instant." If a chronometer be regulated to the time at any place A, and then transported to a second place B, and the local time at B, be determined at any instant, and at that instant the time at A, as shown by the chronometer is noted, the difference of the times is at once known, and that is the difference of longitude required. The principal objection to this plan is that the best chronometers vary. If the variations were constant and regular, and the chronometer always gained or lost a fixed amount for the same interval of time, this objection would disappear. But the variation is not constant, the rate of gain or loss, even in the best instruments, changes from time to time from various causes. Some of these causes may be discovered and allowed for in a measure, others are accidental and unknown. Of the former class are variations due to changes of temperature. At the Naval Observatory, chronometers are rated at different temperatures, and the changes due thereto are noted, and serve to a great extent as a guide in their use. But the transportation of a chronometer, even when done with great care is liable to cause sudden changes in its indications, and of course in carrying it long distances, numerous shocks of greater or less violence are unavoidable. Still, chronometric measurements, when well carried out with a number of chronometers and skilled observers have been very successful. Among notable expeditions of this sort was that undertaken in 1843, by Struve between Pulkova and Altona, in which eighty-one chronometers were employed and nine voyages made from Pulkova to Altona and eight the other way. The results from thirteen of the chronometers were rejected as being discordant, and the deduced longitude was made to depend on the remaining 68. The result thus obtained differs from the latest determination by 0s.2.
The U. S. Coast Survey instituted chronometric expeditions between Cambridge, Mass., and Liverpool, England, in the years 1849, '50, '51 and '55. The probable error of the results of six voyages, three in each direction, in 1855 was 0s.19, fifty chronometers being carried.
Among other methods of determining differences of time may be mentioned the observation of certain celestial phenomena, which are visible at the same absolute instant by observers in various parts of the globe, such as the instant of the beginning or end of an eclipse of the moon, the eclipses of Jupiter's satellites by the shadow of the planet, the bursting of a meteor, and the appearance or disappearance of a shooting star. The difficulty of identifying these last mentioned objects and the impossibility of foretelling their occurrence prevents the extended use of this method.
Terrestrial signals may be used and among these can be included those sent by the electric telegraph. But when two stations are near together a signal may be made at either or at an intermediate station, which can be observed at both, the time may be noted at each of the stations and the difference found directly. These signals may be made by flashes of gunpowder, or the appearance and disappearance of a strong light, or a pre-concerted movement of any object easily seen. The heliotrope reflecting the image of the sun from one station to the other with an arrangement for suddenly eclipsing it, is a useful and efficient apparatus.
Various truly astronomical methods have been employed with good results, of these may be mentioned moon-culminations, azimuths of the moon, lunar distances, etc.
Coming now to the use of the electric telegraph for this purpose the following is a rough outline of the methods employed. Suppose two stations A and B connected by wire, and provided with clocks, chronographs and transit instruments. A list of suitable fixed stars is compiled and each observer furnished with a copy. The observer at A the eastern station, selects a star from his list and sets his transit instrument upon it. He is furnished with a key by which he can send telegraphic signals over the line and also mark the time on his own chronograph. The instant he observes the star crossing the spider line which represents the meridian, he taps his key, thus registering the time on his own chronograph and on that at station B and this operation he repeats with as many stars as necessary. B has his instrument set for the first star, and when it crosses his meridian, he taps his key marking the time on his own chronograph and also on A's. Then, disregarding instrumental and personal errors and the rate of the clock, A has a record of the times at which the star passed both meridians. The difference of these times is the difference of longitude sought, except for an error due to the time occupied in the transmission of the signal over the wire between the stations. B also has a record of the same difference of time with the same error affecting it in the opposite way. A mean of these two differences, will be the true difference with the error of transmission eliminated. This method has the advantage of not depending upon the computed position of the star. The instrumental errors may be allowed for, as well as the rate of the clocks, and the personal error may be eliminated by the exchange of stations.
There are disadvantages inseparable from this method, however, especially when the meridian distance is great. A star observed at the first station, may be obscured by clouds at the time of its meridian passage at the second. And the weather generally, at the two stations may be cloudy, so that while stars can be observed at intervals, yet it may be impossible to note the meridian passage of the same star at both places on the same night. Then the telegraph lines are usually the property of some commercial company and while their use for a short time might be freely granted, yet a protracted occupation of them as necessary when the meridians are distant from each other, would prove a serious hindrance to their regular business.
The method at this time most generally employed, is to observe at each station a number of stars entirely independently of the other. From these stars are deduced the clock errors and rates upon the respective local times. Then at some prearranged period, communication is opened between the stations, and a comparison of the clocks made which shows their exact difference at a given instant. By applying the error to the time as shown by the clock at this instant, the exact local time at each station is the result, and applying the difference between the clocks as shown by the comparison, the required difference of longitude is readily obtained.
These methods originated, as did the electric telegraph, in the United States, and soon after Morse's invention came into practical use, they were extensively employed by the Coast Survey, in accurately determining points in every part of the country that could be reached, no pains being spared to make the determinations as accurate as possible. Upon the completion of the first successful Atlantic cable in 1866, an expedition was organized and placed in charge of Dr. B. A. Gould, for the purpose of measuring the meridian distance between Greenwich and the Naval Observatory at Washington. This was successfully carried out in spite of numerous difficulties, and the result proved that the determinations already made upon which the most reliance was placed were decidedly in error. The result from the chronometric expedition in 1855 previously referred to differing over a second of time.
In constructing charts for use at sea, the accurate determination of latitude and longitude is of the utmost importance. The navigator starting on a voyage must know the exact position of his destination as well as the location of dangers to be avoided. He must know the error and rate of his chronometer when he sets out, but as the rate is not constant he should have some means of re-rating it at any place where he may stop. If the longitude of this place is well determined, the operation of obtaining the error and rate is an easy one, and may save his vessel from loss.