The writer first refers to a series of experiments made under the direction of Professor Bache, for the determination of the difference of longitude between New York, Philadelphia and Washington, by means of the magnetic telegraph. By this series of experiments he considers it established that, by means of Morse’s telegraph, two clocks distant from each other 200 miles, can be compared together with the same precision as if they were placed side by side; and that the difference of longitude of two places can be determined with the same precision as the relative error of the clocks. These results were so satisfactory that Professor Bache determined to prosecute them more extensively, and during the past summer comparisons have been made between New York and Cambridge observatory near Boston. The plan of operation this season was more matured than during the former. The comparisons were all made between a solar chronometer at Cambridge and a sidereal clock at New York. At ten o’clock in the evening, the two observatories having been put in telegraphic communication, when the seconds hand of the solar chronometer came round to 60
s
, a signal was given at Cambridge, by pressing the key of the telegraph-register; at the same instant a click was heard at New York, and the time was recorded according to the sidereal clock. At the end of 10
s
a second signal was given, which was also recorded at New York; at the end of another 10
s
a third signal was given, and so on for sixty seconds. The Cambridge astronomer then commenced beating seconds by striking the key of the telegraph-register in coincidence with the beats of his chronometer. The New York astronomer compared the signals received with the beats of his clock, and waited for a coincidence. When the beats were sensibly synchronous the time was recorded, and the astronomer waited six minutes for another coincidence of beats. The Cambridge astronomer continued beating seconds for
fifteen minutes
, during which time the New York observer was sure of two coincidences, and might obtain three. When these were concluded, the New York astronomer in the same manner gave signals for one minute at intervals of 10
s
, and then beat seconds for fifteen minutes, during which time the Cambridge astronomer obtained four or five coincidences upon his chronometer. This mode of comparison was practised every night, and it is considered that the uncertainty in the comparison of the time-pieces cannot exceed two or three hundredths of a second on any night; and in a series of comparisons the error may be regarded as entirely eliminated. Another mode of comparison which was practised is that of telegraphing star transits. A list of stars which culminate near our zenith at intervals of five or six minutes was prepared, and the observers, both at New York and Cambridge, were furnished with a copy. They then proceeded as follows: Cambridge selected two stars from the list, which we wall call A and B, and struck the key of his register at the instant when the star A passed each of the seven wires of his transit. These signals were heard at New York, and the times recorded. Cambridge then observed the transit of star B in the ordinary manner without telegraphing. New York then observed the transit of star A on his meridian in the usual manner; and struck his key at the instant the star B passed each of the seven wires of his transit, which signals were heard and recorded at Cambridge. The difference of longitude between New York and Cambridge is nearly twelve minutes, affording ample time for all these observations. Thus New York obtained upon his own clock the times of transit of star A over the meridians of Cambridge and New York; and Cambridge obtained upon his chronometer the times of transit of star B over the same meridians. The difference of these times gives the difference of longitude independent of the right ascension of the stars. Both observers then reversed the axis of their transit instruments; Cambridge selected a second pair of stars from the list, and the same series of observations was repeated as with the first pair. The error of collimation was thus eliminated, and by confining the observations to stars within about five degrees of the zenith, the influence of azimuthal error was avoided. The level being read at every reversal, the correction for it was applied by computation. In this manner it is hoped to eliminate every possible source of error, except that which arises from the personal habits of the observers. In order to eliminate this error, a
travelling
observer worked for a time at Cambridge and compared with the Cambridge astronomer; then came to New York and compared with the New York astronomer; then returned to Cambridge again, and so on as often as was thought necessary. Finally, at the conclusion of the campaign all the observers were to meet at Cambridge and make a general comparison of their modes of observation.
Analytical Study of Earth Tides on Low Orbits Satellites
