361 



LONGITUDE AND LATITUDE. 



LONGITUDE AND LATITUDE. 



363 



convenient and possible, at the same altitude morning and evening. 

 We should also recommend when the sun is observed that both 

 limbs should be observed without moving the index. For instance, 

 if in the morning the sun were about 14 high, set the instrument to 

 30, note the instant when the upper limb by reflection touches the 

 upper limb seen in the horizon, read off the angle very carefully, 

 wait till the lower limbs form their contact, and note the time. 

 Then set to 31 30' or 32" and proceed as before, and repeat the 

 operation, having again set forward 1 30' or 2. The observer has 

 then several checks without trouble, for the time in which the sun 

 rises through a diameter will be sensibly equal or vary uniformly ; 

 and in like manner the times of rising through 1 30' or 2 will point 

 out if any of the usual errors have been committed. In the after- 

 noon the same process should be repeated in an inverse order, and 

 the time of apparent noon deduced from each pair.* It is to be 

 understood as a universal rule, that the index error is to be 

 carefully determined, and the barometer and thermometer noted 

 whenever observations of altitude for time or latitude are made. 



3. The same mode of observing equal altitudes might be applied to 

 stars, but the observations would be extended to very inconvenient 

 hours, and it is nearly as accurate to observe two bright stars, one to 

 the east and the other to the west, and if possible at about the same 

 altitudes. Each star will then give an error of the chronometer, and 

 if the altitudes are rightly observed, the same error of the chrono- 

 meter. If the errors do not agree, a mean will come nearer to the 

 truth than either of them separately ; but if the stars have not the 

 same polar distance, the effect of a given error hi altitude upon 

 the hour angle must be computed for each, and the difference 

 between the chronometer's errors divided in this ratio. Thus, sup- 

 pose the eastern star gives a chronometer error of 25''0 fast, and the 

 western star an error of 28"0 fast, while an error of 1' in the altitude 

 of the eastern star causes twice the error in the deduced hour angle 

 that a similar error of 1' does in the western star; the concluded 

 tme error should be 27"0, instead of the mean error 26"5. The 

 reader will see that if the observations are made at exactly the 

 same altitude, any mistake as to the index error, refraction, or any 

 instrumental defect, is thus got rid of without much trouble. But, 

 as has been mentioned before, very perfect observations of stars 

 with reflecting instruments can scarcely be made unless the instal- 

 ment is mounted on a stand. From good sets of observations of a 

 star east and a star west, the time may be determined to 0*'3 or 0"'4. 

 The time is required to reduce circum-meridian observations to the 

 meridian for finding the latitude, and again the latitude is required 

 in order to deduce the time from altitudes. An approximate latitude, 

 such as results from the largest observed altitude about the meri- 

 dian, will give the time near enough for the reduction to the meridian, 

 and then the time may be computed rigorously with the exact latitude. 

 Provision may be made for this revision by taking out the differ- 

 ences of the logarithms at each step of the first computation; but 

 generally speaking, when the altitudes for time aro taken near the 

 prime vertical, as they ought to be, a small error in the latitude 

 has so little effect on the hour angle, that the approximate latitude is 

 near enough. 



Determination of Grci.nwick Time astronomically. 1. There are two 

 phenomena which are seen at the same moment from whatever part of 

 the earth they are visible, namely, a lunar eclipse and the eclipses of 

 Jupiter's satellites. The first was the only phenomenon from which 

 longitudes were derived previous to the invention of telescopes, but it 

 is not of frequent occurrence, and unfortunately cannot be noted very 

 exactly. It has been proposed to measure equal quantities of the 

 eclipse ou each side of the middle, and formerly astronomers were very 

 careful to note the moments when the umbra touched or covered \\vll- 

 defined spots. But at present, lunar eclipses are scarcely regarded, as 

 there are many more accurate means of determining the longitude, and 

 of more frequent occurrence ; and lunar eclipses are of no value in the 

 theory of the moon's motions. The eclipses of the satellites of Jupiter, 

 especially of the first satellite, are much more common, and have been 

 of great use in modern geography. The time at which the eclipses 

 take place, that is, when the satellite, passing into the shadow of 

 Jupiter, is lost (immerges), or passing out of the shadow, becomes 

 rgea), are set down in the ' Nautical Almanac ' at the time 

 they would be seen at Greenwich if visible. The observer at any 

 other place nutcs when this phenomenon does actually happen at the 

 place . ion, and the difference between the two times is the 



i ule of the place from Greenwich ; east if the time of the eclipse 

 in later than at Greenwich, and west if it be earlier. Unfortunately 

 this method, so easy in practice, in by no means as accurate as it might 

 at first sight appear. The theory of the satellites is scarcely to be con- 

 sidered as perfect, b\it this objection might be obviated by comparing 

 corresponding observations, and might be very much diminished by 

 correcting the predictions of the ' Nautical Almanac ' by observations 

 made at Greenwich, or any other well known place, about the same 

 time. But the phenomenon is a gradual and not an instantaneous one, 

 and the appearance or disappearance of the satellite varies greatly with 

 the goodness of the telescope, the eye or mood of the observer, the 



There are tables for this purpose in Schumacher'* ' Jlulfstufdn,' and in 

 man/ Kit of ttiblci. 



atmosphere at the place of observation, &c., so that a longitude 

 deduced from an eclipse of the first satellite may be considerably wide 

 of the truth. With ordinary telescopes we believe that eclipses of the 

 second satellite are more than twice as uncertain as the first, and that 

 the third and fourth satellites are not worth observing for this pur- 

 pose, being mxich inferior to good lunar distances. A large mass of 

 eclipses of Jupiter's satellites made by the same telescope and the same 

 observer, and where the immersions are nearly as numerous as the 

 emersions, will however yield a satisfactory result. The aperture of 

 the object-glass employed, and also the sight of the observer, should 

 correspond as nearly as possible with the telescope aud observer at 

 Greenwich, or whatever place is adopted as a standard of comparison. 

 It is not considered advisable to use a smaller telescope than an 

 achromatic of 2| inches aperture for this purpose, or one larger than 

 of 3^ aperture. 



2. The -time at Greenwich is most accurately determined by solar 

 eclipses or occultatious of fixed stars by the moon. The computations 

 are rather long, but not very difficult or abstruse. The beginning and 

 end of the solar eclipse should be observed ; the latter is the better 

 marked phenomenon, and if the eclipse be annular, the commencement 

 and breaking up of the annulus. Recent observations have shown that 

 these appearances are not instantaneous, and therefore that longitudes 

 deduced from them are not free from uncertainty. The occultation of 

 a fixed star by the moon is not liable to this objection ; and when the 

 star is bright, and both immersion and emersion can be carefully 

 observed, the longitude from an occultation affords perhaps the best 

 determination possible of the longitude between two distant places. 

 Yet even here doubts may arise, at least in some cases. The star may 

 be occulted too early by a lunar mountain, or disappear too late in a 

 lunar valley. The occultation should be observed at both places, 

 which is not often possible, and the star should pass not far from the 

 centre of the moon. If the solar eclipse or the oceultation be not 

 observed at Greenwich, or at any well determined observatory, the 

 data of the ' Nautical Almanac ' must be corrected by the meridian 

 observations of the moon about the time. The tables of the sun are 

 at present nearly as perfect as observation can make them, but tho 

 moon may be out 15", or even 20", which might occasion an error of 

 30* or 40" in the deduced longitude, or from an eighth to a sixth of 1. 

 The solar eclipses, &c., with a map showing in what parts of the globe 

 they are visible, are given in the ' Nautical Almanac," and the occulta- 

 tions by the moon of all fixed stars to the sixth magnitude inclusive, 

 visible at Greenwich, are also predicted to the nearest minute, with 

 such a description of the relative situation of moon and star as will 

 enable any one to observe them without difficulty. All possible 

 occultations of fixed stars to the fifth magnitude inclusive, visible any- 

 where, are also set down in that valuable work, with the data neces- 

 sary for determining whether they are visible at any specified place. 

 We cannot press too earnestly on all persons interested in perfecting 

 geography, the absolute necessity of learning to observe an occultation, 

 and to take altitudes methodically with a circle or sextant. The com- 

 putations may be made at home. 



The transits of Mercury over the sun are rare, and the longitudes 

 derivable from them not very accurate. 



3. A good and now fashionable method of determining the longitude 

 is by observing with a transit instrument the meridian passage of the 

 moon's bright limb, and of stars which are near her parallel of declina- 

 tion. The ' Nautical Almanac ' contains a list of the stars proper to 

 be observed with the moon, and also the variations of the moon's E. A. 

 in one hour, of longitude, for computing the longitude.* When the 

 place of observation is tolerably near Greenwich, the computation is 

 very simple, that is, if the transit ii nearly in the meridian and the moon 

 is observed all over the wires. The error of the chronometer is taken 

 from the neighbouring stars, and the transit of the moon corrected for 

 this error, and for the rate, if sensible. If the place be to the east of 

 Greenwich, the R. A. of the moon is less ; if to the west, the R. A. is 

 greater than at Greenwich. Taking the difference between the R. A. 

 at the pLice aud at Greenwich, and dividing by the variation in one 

 hour of longitude, you have the longitude of the place E. or W. in 

 hours and decimals of an hour. But this result requires correction 

 when the corresponding observations at Greenwich, Cambridge, Edin- 

 burgh, &c., can be procured ; for the R. A. of the moon may be 

 erroneous more than l''Ufrom the imperfection of the lunar tables. 

 By using the R. A. of the moon and stain observed at Green- 

 wich, the longitude will not be affected by the errors of the tables. 

 It is pretty much the same thing, and at times more convenient, 

 to let the former computation stand, aud to compute the longitude 

 of Greenwich, Cambridge, &c., from the observations respectively 



* These data might perhaps be further extended with advantage. Suppose 

 the H. A. of the moon's bright limb on the meridian of Greenwich to be m ; on 

 tho meridian of any other place the longitude of which is required, m' ; the 

 longitude of the place to be /, + when west, and east; then m' can he thus 

 expressed; m' == m 4- a I -f b I* + c / 3 -f d /*, where a, 6, c, and d can be 

 previously computed, I being in decimals of u day. The approximate value of I, 



tri in 

 from the first term, = . Substituting this value for I, let the sum cf the 



other terms = , then the exact longitude 



