and days will he experience. But if he travel once round the globe in the direction of its motion, he will, on his arrival, have really made one turn more round its centre; and if in the opposite direction, one turn less than if he had remained upon one point of its surface: in the former case, then, he will have witnessed one alternation of day and night more, in the latter one less, than if he had trusted to the rotation of the earth alone to carry him round. As the earth revolves from west to east, it follows that a westward direction of his journey, by which he counteracts its rotation, will cause him to lose a day, and an eastward direction, by which he conspires with it, to gain one. In the former case, all his days will be longer; in the latter, shorter than those of a stationary observer. This contingency has actually happened to circumnavigators. Hence, also, it must necessarily happen that distant settlements, on the same meridian, will differ a day in their usual reckoning of time, according as they have been colonized by settlers arriving in an eastward or in a westward direction, -a circumstance which may produce strange confusion when they come to communicate with each other. The only mode of correcting the ambiguity, and settling the disputes which such a difference may give rise to, consists in having recourse to the equinoctial date, which can never be ambiguous.

(258.) Unfortunately for geography and navigation, the chronometer, though greatly and indeed wonderfully improved by the skill of modern artists, is yet far too imperfect an instrument to be relied on implicitly. However such an instrument may preserve its uniformity of rate for a few hours, or even days, yet in long absences from home the chances of error and accident become so multiplied, as to destroy all security of reliance on even the best. To a certain extent this may, indeed, be remedied by carrying out several, and using them as checks on each other; but, besides the expense and trouble, this is only a palliation of the evil the great and fundamental, as it is the only one to which the determination of longitudes by time-keepers is liable. It becomes necessary, therefore, to resort to other means of communicating from one station to another a knowledge of its local time, or

of propagating from some principal station, as a centre, its local time as a universal standard with which the local time at any other, however situated, may be at once compared, and thus the longitudes of all places be referred to the meridian of such central point.

(259.) The simplest and most accurate method by which this object can be accomplished, when circumstances admit of its adoption, is that by telegraphic signal. Let A and B be two observatories, or other stations, provided with accurate means of determining their respective local times, and let us first suppose them visible from each other. Their clocks being regulated, and their errors and rates ascertained and applied, let a signal be made at A, of some sudden and definite kind, such as the flash of gunpowder, the explosion of a rocket, the sudden extinction of a bright light, or any other which admits of no mistake, and can be seen at great distances. The moment of the signal being made must be noted by each observer at his respective clock or watch, as if it were the transit of a star, or any astronomical phenomenon, and the error and rate of the clock at each station being applied, the local time of the signal at each is determined. Consequently, when the observers communicate their observations of the signal to each other, since (owing to the almost instantaneous transmission of light) it must have been seen at the same absolute instant by both, the difference of their local times, and therefore of their longitudes, becomes known. For example, at A the signal is observed to happen at 5h 0m 0 sid. time at A, as obtained by applying the error and rate to the time shown by the clock at A, when the signal was scen there. At B the same signal was seen at 5h 4m 03, sid. time at B, similarly deduced from the time noted by the clock at B, by applying its error and rate. Consequently, the difference of their local epochs is 4m 0s, which is also their difference of longitudes in time, or 1° 0′ 0′′ in hour angle.

(260.) The accuracy of the final determination may be increased by making and observing several signals at stated intervals, each of which affords a comparison of times, and the mean of all which is, of course, more to be depended

on than the result of any single comparison. By this means, the error introduced by the comparison of clocks may be regarded as altogether destroyed.

(261.) The distances at which signals can be rendered visible must of course depend on the nature of the interposed country. Over sea the explosion of rockets may easily be seen at fifty or sixty miles; and in mountainous countries the flash of gunpowder in an open spoon may be seen, if a proper station be chosen for its exhibition, at much greater distances.

(262.) When the direct light of the flash can no longer be perceived, either owing to the convexity of the interposed segment of the earth, or to intervening obstacles, the sudden illumination cast on the under surface of the clouds by the explosion of considerable quantities of powder may often be observed with success; and in this way signals have been made at very much greater distances. Whatever means can be devised of exciting in two distant observers the same sensation, whether of sound, light, or visible motion, at precisely the same instant of time, may be employed as a longitude signal. Wherever, for instance, an unbroken line of electrotelegraphic connection has been, or hereafter may be, established, the means exist of making as complete a comparison of clocks or watches as if they stood side by side, so that no method more complete for the determination of differences of longitude can be desired. The differences of longitude between the observatories of New York, Washington and Philadelphia have been very recently determined in this manner by the astronomers at those observatories.

(263.) Where no such electric communication exists, however, the interval between observing stations may be increased by causing the signals to be made not at one of them, but at an intermediate point; for, provided they are seen by both parties, it is a matter of indifference where they are exhibited. Still the interval which could be thus embraced would be very limited, and the method in consequence of little use, but for the following ingenious contrivance, by which it can be extended to any distance, and carried over any tract of country, however difficult.

(264.) This contrivance consists in establishing, between the extreme stations, whose difference of longitude is to be ascertained, and at which the local times are observed, a chain of intermediate stations, alternately destined for signals and for observers. Thus, let A and Z be the extreme stations. At B let a signal station be established, at which rockets, &c. are fired at stated intervals. At C let an observer be placed, provided with a chronometer; at D, another signal station; at E, another observer and chronometer; till the whole line is occupied by stations so arranged, that the signal at B can be seen from A and C; those at D, from C and E; and so on. Matters being thus arranged, and the errors and rates of the clocks at A and Z ascertained by astronomical observation, let a signal be made at B, and observed at A and C, and the times noted. Thus the difference between A's clock and C's chronometer becomes known. After a short interval (five minutes for instance) let a signal be made at D, and observed by C and E. Then will the difference between their respective chronometers be determined; and the difference between the former and the clock at A being already ascertained, the difference between the clock A and chronometer E is therefore known. This, however, supposes that the intermediate chronometer C has kept true sidereal time, or at least a known rate, in the interval between the signals.

Now this interval is purposely made so very short, that no instrument of any pretensions to character can possibly produce an appretiable amount of error in its lapse by deviations from its usual rate. Thus the time propagated from A to C may be considered as handed over, without gain or loss (save from error of observation), to E. Similarly, by the signal made at F, and observed at E and Z, the time so transmitted to E is forwarded on to Z; and thus at length the clocks at A and Z are compared. The process

may be repeated as often as is necessary to destroy error by a mean of results; and when the line of stations is numerous, by keeping up a succession of signals, so as to allow each observer to note alternately those on either side, which is easily pre-arranged, many comparisons may be kept running along the line at once, by which time is saved, and other advantages obtained. In important cases the process is usually repeated on several nights in succession.

*

(265.) In place of artificial signals, natural ones, when they occur sufficiently definite for observation, may be equally employed. In a clear night the number of those singular meteors, called shooting stars, which may be observed, is often very great, especially on the 9th and 10th of August, and some other days, as November 12 and 13; and as they are sudden in their appearance and disappearance, and from the great height at which they have been ascertained to take place are visible over extensive regions of the earth's surface, there is no doubt that they may be resorted to with advantage, by previous concert and agreement between distant observers to watch and note them. † Those sudden disturbances of the magnetic needle, to which the name of magnetic shocks has been given, have been satisfactorily ascertained to be, very often at least, simultaneous over whole continents, and in some, perhaps, over the whole globe. These, if observed at magnetic observatories with precise attention to astronomical time, may become the means of determining their differences of longitude with more precision, possibly, than by any other method, if a sufficient number of remarkable shocks be observed to ascertain their identity, about which the intervals of time between their occurrence (exactly alike at both stations) will leave no doubt.

For a complete account of this method, and the mode of deducing the most advantageous result from a combination of all the observations, see a paper on the difference of longitudes of Greenwich and Paris, Phil. Trans. 1826; by the Author of this volume.

†This idea was first suggested by the late Dr. Maskelyne, to whom, however, the practically useful fact of their periodic recurrence was unknown. Mr. Cooper has thus employed the meteors of the 10th and 12th August, 1847, to determine the difference of longitudes of Markree and Mount Eagle, in Ireland. Those of the same epoch have also been used in Germany for ascertaining the longitudes of several stations, and with very satisfactory results.

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