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to such if observed with a chronometer regulated to mean time. When, instead of the two or three chronometers generally taken on board every ship, a number of these instruments, whose rates and errors have been previously carefully ascertained, are conveyed from one meridian to another, the comparison of the mean of the times shown by the chronometers with the local time at each place, affords the means of determining with considerable accuracy the difference of their longitudes; this mode is much practised at present on board surveying vessels *, for measuring the respective meridian distances between a number of maritime towns, ports, and other places on the sea-coast of distant countries. On shore the difference of longitude between two stations can also be determined with precision by the transmission of pocket chronometers between them; provided the errors of the box chronometers or clocks at these stations on sidereal time, and their rates, have been carefully ascertained by transit observations. Where the distance is not very considerable, the operation consists simply in comparing several pocket chronometers with the standard instrument at one of the stations, and then sending them † with the greatest care to be compared with the clock or chronometer at the other station, to be returned immediately for another comparison at the starting point; which process of transmission should be repeated several times.
When the time occupied by this operation is considerable, more than four or five days for instance, the accuracy of the result will be increased by stationing a careful assistant at a post midway between the two extreme stations with a box chronometer, with which the transmitted pocket chronometers are to be compared. Mr. Airy recommends commencing from this central position, sending the pocket chronometers (divided into two batches) simultaneously for comparison to the two principal extreme stations, and comparing them again on their return, at nearly the same time, at the intermediate point; by which modification, the time through
* On board H. M. S. Beagle, employed as a surveying vessel principally on the coasts of Australia and Van Diemen's Land, there were at one time as many as twenty-one first-rate chronometers.
This should be done directly after the error of the standard chronometer has been tested by observations with the transit instrument.
which reliance is placed upon the pocket chronometers is diminished one-half, and very little dependence is made to rest upon the steadiness of performance of the box chronometer at the central place of observation.
This method of obtaining the difference of longitudes of two distant places would, it is imagined, seldom be resorted to where the distance was very great, and where an intermediate station was found necessary. On the North American Boundary Survey, the second method was never tried, but the first and more simple process of direct transmission and comparison between the two stations was constantly practised with great success. One example has been selected from Major Robinson's report, calculated according to the directions drawn up by Mr. Airy, each of the three comparisons recorded being the mean of six observations.
Second Intermediate Comparison.
CALCULATION FOR DIFFERENCE OF LONGITUDE BETWEEN ST. HELEN'S ISLAND, MONTREAL, AND ST. REGIS.
Third Comparison (on return).
Standard Chronometer (943) Pocket Chronometer
2 56 20 50
In comparing chronometers, two persons are generally employed, one of whom watches the seconds hand of one instrument until it arrives at some convenient division, such as the commencement of a minute, or one of the ten seconds, when he gives the signal to "stop" to the other, whose attention has been meanwhile fixed upon the seconds hand of the other chronometer. Where one person alone makes the comparison, his only plan is to register the seconds, and then the minutes and hour of one instrument, commencing to count the beats 1, 2, 3, &c., from the moment selected by him (whilst he is writing down the time observed), and then to transfer his eye to the other chronometer, continuing to count the beats until he observes its second hand opposite some marked number of seconds, when he stops; writing down first the number of beats counted, and then the seconds, minutes, and hour of the second chronometer; the number of beats is of course to be subtracted from this for the comparison of the time shown by the first instrument.
When a chronometer adjusted to mean solar time is to be compared with one going sidereal time, or with a sidereal clock, the only correct method with one observer is by the coincidence of their beats, in the manner described by Mr. Airy.
When the chronometer going mean solar time has a half-second beat, and the other instrument or the clock a second's beat, they will appear at the end of every second to beat (after some little time) almost simultaneously. Select one that appears perfectly coincident, and commence counting the beats 1, 2, 3, &c., of the clock or sidereal chronometer, writing down at the same time the second, minutes, and hour of the solar one; then turn your eye to the seconds hand of the clock or other chronometer, continuing counting till the seconds hand is at some conspicuous place, and then stop. Write down first the number of seconds you have counted; then the seconds on the clock face at which you stopped; and lastly, the minutes and hour; then the comparison will stand thus:—the time observed by the first chronometer = time observed by the second (or the clock as it may be), minus the number of beats counted.
When the solar time chronometer and the sidereal have both half-second beats, the process is the same, counting every alternate
beat of the sidereal instrument. With a chronometer going mean solar time, and having a beat of five times in two seconds (a very common one, particularly in pocket chronometers), the beats will only coincide with the divisions upon the dial every alternate second, each beat being equivalent to 0.4; the process of comparison is, however, much the same as that already detailed, but it will be facilitated by marking distinctly with ink upon the face of the chronometer every other second, unless this has been originally so divided as to render the precaution unnecessary.
The following example shows the method of deducing the error of a chronometer going mean solar time, by comparison with a sidereal clock whose rate and error are known by transit observations.
0 0 0.35 Correction for longitude 2m 9s east.
20 11 46.55 Sidereal time at mean noon at place of observation. 17 13 0 Clock at time of comparison.
2 58 46.55
1 59 40-34
0 57 50.49
0 0 45-87 Equivalents in mean solar time for above difference.
0 0 0.54
2 58 17.24 Mean interval from noon by clock.
0 2 22-17 Error of chronometer, slow.
The eclipses of Jupiter's satellites are phenomena of very frequent occurrence, the precise instants of which can be calculated with