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5 58 43-18
CALCULATION FOR DIFFERENCE OF LONGITUDE BETWEEN ST. HELEN'S ISLAND, MONTREAL, AND ST. REGIS.
Second Intermediate Comparison.
5 43 56.82 23 43 0.
6 0 56.82
22 20 44
2 0 6
Reading of 943
Sidereal Time by 943
6 6 19.76 5 58 43.18
0 7 36.58
Rate, losing 2.17 per diem for 32 hours
True Sidereal Time by 943.
Difference of Longitude
Standard Chronometer (341)
Date of Return
2 44 10.92
Difference at first Comparison
Add proportional part of intermediate interval
6 0 56.82
0 2 2.48
2 39 41-45
4 29-47 St. Regis, west of St. Helen's Station.
Intermediate interval 1 2 54
Intermed. date of Comparison. 23
Corresponded to Reading of 341
Rate, gaining 1.19 per diem for 59 hours
True Sidereal Time by 2187
2 40 40-70
0 56.330 2.92
2 39 41-45
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 ob
20 11 46.90 Sidereal time.
Greenwich mean noon.
0 0 0.35 Correction for longitude 2m 9s east.
1 42.76 Mean time A.M. by clock. 905 Time by chronometer.
20 11 46.55 Sidereal time at mean noon at place of observation.
17 13 0 Clock at time of comparison.
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.
12 0 0
1 37-76 Chronometer slow (relatively).
0 0 44-41 Clock slow.
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
certainty for Greenwich time; but a telescope magnifying at least forty times is required for their observation; and those of different powers are found to give such different results as to the moment of immersion or emersion, that the method is not susceptible of the accuracy it would appear to promise, and is moreover almost impracticable at sea. In determining the longitude by this method, the local time must be found by observations of one or more fixed stars, unless it is known from a chronometer whose error and rate has been previously ascertained.
The eclipses of the sun and moon also enable us to determine the longitude; the former with considerable accuracy; but their rare occurrence renders them of little or no practical benefit, and the results obtained by the eclipses of the moon are generally unsatisfactory, owing to the indistinct outline of the shadow of the earth's border.
The three methods upon which the most dependence can be placed, are 1st, by a "lunar observation," which, as before stated, possesses the great advantage of being easily taken at sea; 2ndly, by the meridional transits of the moon, compared with those of certain stars previously agreed on, which are given in the Nautical Almanac under the head of " Moon Culminating Stars ;" and 3rdly, by occultations of the fixed stars by the moon.-The two latter methods are the most accurate of any, but the first of them requires the use of a transit instrument, and the latter a good telescope; both involve also long and intricate calculations, which will be found fully detailed in the works of Dr. Pearson, and in chapter 37 of Woodhouse's Astronomy. The methods given in the following pages considerably shorten the labour of the more accurate computations, and are the same as those in Mr. Riddle's "Navigation."
* The time occupied by light in travelling from the sun to the earth is also ascertained by means of the eclipses of Jupiter's satellites.
The difference of distance the light has to travel from Jupiter to the earth, on the occasion of an eclipse of one of the satellites, happening when they are in opposition or in conjunction, is evidently the major axis of the earth's orbit. This difference has been ascertained to be 16m 263.4, which gives 8m 135.2 for the time occupied by light in passing from the sun to the earth.
The distance of the sun from the earth was determined by means of the transit of Venus over the sun's disc.
Method 1st.-By a Lunar Observation.
The observations for this method of ascertaining the longitude of any place can be taken by one individual; but as there are three elements required as data, which, if not obtained simultaneously, must be reduced to what they would have been if taken at the same moment of time, it is better, if possible, to have that number of observers.
The lunar distance, which is of the first importance, is measured by bringing the enlightened edge of the moon and the star, or the edge of the moon and either limb of the sun, in perfect contact. The other observations required are, the altitudes of the moon, and that of the other object, whether it be the sun, a fixed star, or a planet*; and as these are only taken for the purpose of correcting the angular distance, by clearing it from the effects of parallax and refraction, they do not require the same accuracy, or an equal degree of dexterity in observing. When the observations are made consecutively by one person, the two altitudes are first taken (noticing of course the times); then the lunar distance repeated any number of times, from whence a mean of the times and distance is deduced; and afterwards the altitudes again in reverse order, which altitudes are to be reduced to the same time as that of the mean of the lunar distances.
It being of great moment to simplify and render easy the solution of this problem, which is of the most vital importance at sea, a number of celebrated practical astronomers have turned their attention to the subject, and tables for "clearing the lunar distance" are to be found in all works on Nautical Astronomy, by the use of which the operation is undoubtedly very much shortened+; but as none of these methods show the steps by which this object is attained, the example given below is worked out by spherical trigonometry, and the process will be rendered perfectly easy and intelligible by the following description :
* These altitudes, if not observed, can be calculated when the latitude is known; by which method more accurate results are obtained.
Dr. Pearson enumerates no less than twenty-four astronomers who have published different methods of facilitating the "Clearing the Lunar Distance."