TO REGULATE A CHRONOMETER BY MEANS OF A TRANSIT INSTRUMENT. THIS method excels all others in brevity and accuracy; but it can only be used on shore, and with the transit instrument that has been adjusted with the greatest possible care, so as to have the motion of the line of collimation of the telescope perfectly in the plane of the meridian. We have already given, from pages 145 to 152, the methods of making these adjustments, and of observing these transits; we shall now insert several examples for illustration. To determine the time by the sun's transit over the middle wire of the telescope. In observations of this kind, we must note, by the chronometer, the times of the transit of the first and second limbs of the sun over the meridian wire; the mean of the two observations will be the time of apparent noon, by the chronometer. Then the equation of time is to be taken from the Nautical Almanac for the apparent noon at Greenwich, and the correction applied to it for the longitude of the place of observation, which is easily obtained by the means of the horary variation given in the same work. Applying this equation to the apparent time, by adding or subtracting, according to the directions in the Nautical Almanac, we get the mean time of apparent noon. The difference between this time and the time by the chronometer, will be the error of the chronometer in mean time; moreover the difference between the time by the chronometer and 12h, will be the error of the chronometer for apparent time. EXAMPLE I. Near noon, at the commencement of the 29 of January, 1836, according to the astronomical computation of time, in a place 30°, or 2", west of Greenwich, observed the transits of the limbs of the sun over the meridian wire of the transit instrument, for the purpose of regulating a chronometer. It is required to find, from these observations, the error of the chronometer, either for apparent or mean time. Transit of the first limb by the chronometer... 115610.5 11 58 27.0 2) 14 37 .5 Half-sum is the time of apparent noon by the chronometer..... ..... Equation of time at the place of observation.. Apparent time of observation at noon..... Mean time of observation ..... ......add .add .... .... Hence it appears, that the chronometer is too slow for apparent time 11 57 18.7 13m 21.63 .86 13 22.5 12 00 00 .0 12 13 22 .5 2 41 .3 16 03.8 EXAMPLE II. In another observation of the sun's transit, similar to the preceding, made June 25, 1836, in the longitude of 60°, or 4", east, we shall suppose that the time of the Equation of time by Nautical Almanac at apparent noon at Greenwich 2m 14 34 2.12 2 12 2 .add 12 00 00.0 12 02 12.2 Mean time of observation..... Hence it appears, that the chronometer is too fast for apparent time 3m 18.9 1 06.7 To determine the time by the sun's transit, observed at the five wires of the telescope. If the telescope of the transit instrument be furnished, as usual, with five equidistant and parallel wires, two on each side of the meridian wire, we can, with very little extra time or trouble, make the observations of the transits of the first limb of the sun at all the wires, and mark down the corresponding times by the chronometer, in five separate columns, on the same horizontal line, from left to right. Immediately afterwards, make the observations of the transits of the second limb of the sun, over the same wires, and mark these times below the former numbers respectively, taking them in a contrary order, or from right to left. The sums of the two numbers in each of the five columns will be nearly the same, and the mean of the whole will be the time of the transit of the sun's centre over the meridian, as shown by the chronometer. Comparing this with the time of apparent noon, 12, we get the error of the chronometer for apparent time; or by comparing it with the mean time of noon, we get the error of the chronometer for mean time, as in the two preceding examples. First limb.... Second limb.... EXAMPLE III. July 23, 1836, in the longitude of 74°, or 4h 56m, W., the following observations of the times of the transit of the sun's limbs over the wires of the transit instrumen were made. Required the error of the chronometer for mean time. * We have already remarked, in page 150, that the wires are so fixed in the telescope, that the first limb of the sun passes over all of them before the second limb arrives at the first wire. This equality in the sums renders it unnecessary to write down the hours of the observation, except in the middle column; and we may also neglect, in the column of minutes, the figures which stand for 14.3 10)70.7 12h 07m 07.07 12 06 07 .61 Corr. 4h 56m X0.059 29 Equation of time. 6 07.61 12b 12 6 07.61 EXAMPLE IV. May 14, 1836, in the longitude of 45°, or 3", east, the following transits of the sun's limb over the wires of the transit instrument, were observed. Required the error of the chronometer for mean time. To determine the time by the transit of a fixed star over the meridian. In observations with the transit instrument, it is most commonly the case, that the chronometer which is used in making the observations, will give the mean time at Greenwich within a few seconds;* and for this time we must find, in the Nautical Almanac, the sun's right ascension and that of the star. Subtracting the former from the latter, (increased by 24 when necessary,) we get the apparent time of the star's transit over the meridian; and by applying to it the equation of time, taken from the Nautical Almanac, for the above time at Greenwich, we obtain the mean time at the place of observation. The difference between this and the time of the transit, as noted by the chronometer, will represent its error. We may, as in observations of the sun, use the middle wire only, and note the time of the transit, when the star is bisected by that wire; or, with greater chance of accuracy, we may take the mean of the observed times of passing the five wires, as a more correct time of the actual transit. To illustrate this, we shall give the following examples: EXAMPLE V. July 24, 1836, in the longitude of 44° 39′, or 2h 58m 363, east, observed the transit of the star Arcturus over the middle wire of the telescope, the time by the chronometer, which was supposed to be regulated very nearly for mean time in the meridian of Greenwich, being 3h 00m 10. Required the mean time of the transit at the place of observation. 's right ascension at noon, at Greenwich, by Nautical Almanac.. 8h 15m 05*.79 Correction for 3h 00m 10" X 9.891...... 's right ascension at the estimated time at Greenwich Star's right ascension at the same time, by Nautical Almanac.. 29.70 8 15 35.49 14 08 12.13 Subtract 's right ascension, gives the apparent time of observation 5 52 36.64 When we have no good regulation of the chronometer, from Greenwich, we must estimate the time at that place, from the supposed time at the place of observation, by applying to it the longitude; adding when west, or subtracting when east; repeating the operation if we should find, after calculating the observations of the transit, that any essential error was made in the time at the place of observation EXAMPLE VI. March 10, 1836, in the longitude of 17° 18', or 1h 09m 12', east, observed the transit of the star Sirius over the five wires of the telescope, at the times by the chronometer as given below; the chronometer being supposed to give very nearly the mean time at Greenwich. Required the mean time of this transit at the place of observation. 's right ascension at noon, at Greenwich, by the Nautical Almanac 23h 23m 10.85 Correction for 6h 14m 56 X 9.186..... 's right ascension at the estimated time at Greenwich.... Subtract's right ascension, gives the apparent time of observation Corrected equation of time Mean time of observation ....... 10m 25".45 10 21 .28....add 57.40 23 24 08 25 30 37 55.39 7 13 47.14 10 21..28 7 24 08.42 6 14 56.00 Time by the chronometer Error of the chronometer for mean time... 109 12.42 0 58 51.14 We may in the same way find the time by a transit of the planet, either by taking the mean of the times of the transits of the two limbs of the planet across the middle wire, or the mean of the times of the limbs passing all the wires; then the calculation is to be made, as in Examples V. VI.; taking from the Nautical Almanac, and using the right ascension of the planet, instead of that of the star. This method is so plain, that it will not be necessary to give any examples. The transit of the moon might also be used; but the calculation becomes so complex, on account of the rapidity of her motion, that it is wholly inexpedient to use such observations for regulating a chronometer. LUNAR OBSERVATIONS. ALMOST all the methods of determining the difference of longitude between any two places, depend on the general principle of finding the difference between the times of taking any observation, estimated under the meridian of both those places. For, in any place, it is the time of apparent noon when the sun is on the meridian; and as the sun, by his diurnal motion, appears on the meridian of Greenwich (from which the longitude is reckoned) one hour earlier than in a place in 15° west longitude, and one hour later than in a place in 15° east longitude, and in proportion for a greater or less longitude, it follows that, if, at the time of taking an observation, the corresponding time at Greenwich be known, the longitude of the place of observation will be found by allowing 15° for every hour of difference between those times, the longitude being east when the time at Greenwich is earlier than at the place of observation, otherwise west. It is immaterial whether the times at both places be estimated for apparent or mean time, as the interval is the same when both are apparent as when both are mean; it is, however, universally the practice, at present, to use mean time in all these calculations. Now, an observer, at any place, may determine the apparent or mean time at any moment, by a watch regulated by any of the preceding methods; and if, at the same moment, the apparent or mean time at Greenwich could be obtained, nothing more would be necessary for determining the longitude. One method of determining the time at Greenwich is by a watch regulated to Greenwich time; for it is evident that if a watch could be so constructed as to go uniformly at all times, and in all places, an observer, furnished with a watch thus regulated, would only have to compare the time at the place of observation with the time at Greenwich, shown by the watch, and the difference of the times would give the difference of longitude. This method is useful in a short run; but in a long voyage, implicit confidence cannot be placed in an instrument of such a delicate construction, and liable to so many accidents. Another method of determining the longitude, is by observing the beginning or end of an eclipse of the moon, or the satellites of Jupiter, and taking the difference between the mean time of observation and the mean time given in the Nautical Almanac for the meridian of Greenwich; it being evident that such an eclipse must be observed at both places at the same moment of absolute time; consequently the difference of the times will be the difference of longitude. An observation of an eclipse of the sun, or an occultation, after making allowance for parallax, &c., as taught in the Appendix to this work, may be used in like manner; and this is a very accurate method. However, observations of eclipses are but of small practical utility at sea; for those of the sun and moon happen too seldom, and the difficulty of observing the eclipses of Jupiter's satellites prevents that method from being made use of. In the present improved state of the Nautical Almanac, we may easily determine the longitude on shore, by means of a transit instrument, by observing the time of the moon's transit over the meridian, or by observing the difference between the time of the moon's transit and that of some well-known and near star. Other methods of finding the longitude at sea have been proposed, but among them all there is not one of such practical utility, as that by measuring the angular distance of the moon from the sun, or from certain fixed stars situated near the ecliptic, usually called a lunar observation, or, more frequently, "a lunar." For observations of this kind may be taken, in fair weather, at all times (except near the time of new moon) when the objects are more than 80 or 10° above the horizon; and as the moon moves in her orbit about 1' in 2 of time, it follows that, if her angular distance can be ascertained from the sun or star within 1', the time at Greenwich will be known within 2 minutes, and the longitude within 30 miles. Because the sun, by his apparent diurnal motion, describes 360 degrees in 24 hours, which makes 15 degrees in an hour. |