toxorruDK AKD LATITUDE. 



LONGITUDE AND LATITUDE. 



there, taking care to note UM aigni of the resulting longi- 

 . Than U UM longitudes of UM known and of the unknown 

 . are U*h ** or both we*t, the difference will be the true longi- 

 T^ of UM unknown place, east or west of the known one. BOOM 

 stUtfufii give a larger image of the mono than others, and iti apparent 

 dbaetarb affected by varying the aperture of the objectglats. The 

 laMiIlM enon in UM longitude are got rid of by observing the second 

 lamb as often, if poudbk.M UM tint, and then, keeping the results 

 tcnarau, by taking a mean of UM two. There b a mistaken notion 

 among many observer*, that there u no need to care for the position of 

 UMtnnut. Now any considerable error in the position of the transit 

 doe* occasion an equivalent error in the longitude, and though it can 

 be corrected, U there are data for determining the want of adjustment, 

 I trouble in the computation. It is so easy to place a 

 r in the meridian, and to adjust it in every respect, at 

 ly, that there b no excuse for careletmeas in thin 

 The observer ahould always take the transits of a star near 

 UM* pole, and of all Greenwich atari above and below the moon which 

 pa** about the time of her culmination, and it b proper to reverie the 

 Instrument on alternate nights. When the place of observation is very 

 distant from Greenwich, it will be necessary, until the quantities a, b, 

 e. a*, mentioned in UM note, be computed, to take a little more trouble. 

 The approximate longitude b "nli*iihtH as before, and then the H. A. 

 of the moon's bright limb must be computed for the corresponding 

 Greenwich time, from the R. A. of the moon for every hour ; the 

 moon'* enu-diauieter in R. A. must also be computed. We have found 

 it on the whole nuwt intelligible, and therefore most safe, to compute 

 the R. A. of the moon's bright limb on two hypotheses of longitude, 

 one the minute above and the other the minute below the approximate 

 value, Thete results are to be corrected by the Greenwich or other 

 observations for the error of the lunar tablet, and then, by simple pro- 

 portion, the correction u determined for one of the hypothetical longi- 

 tude*. This b rather a long process, but it is strictly accurate, and 

 UM step* are intelligible a* the computer proceeds. The method of 

 determining the longitude by transits of the moon and stars is the best 

 f distant in latitude or longitude, where the same occulta- 

 It is nearly as good for the most distant as the 

 sat place, the variation of the error of the lunar tables being the 

 only additional cause of inaccuracy, and the phenomenon presents 

 iUeJf very often. It does however require a very nice and well fixed 

 iiMtrument and a careful observer, as 1* error in observing the U. A. of 

 the moon will cause an error of nearly 30* in the resulting longitude, 

 or | of a degree. A considerable mass of observations of both limbs 

 corrected by corresponding observations will scarcely be more than 2* 







4. But where a transit instrument cannot be carried, or cannot l>e 

 used, at at tea, the longitude must be found atlronontifally by the 

 distance of the moon from the sun, planets, or fixed stars, measured 

 with a reflecting instrument. This apparent distance is reduced to the 

 true disttnon, that b, such as it would be, seen from the centre of 

 the earth, and at these distance! are computed and set down in the 

 ' Nautical Almanar, ' for every three hours Greenwich time, as they 

 would be seen from the same place, the Greenwich time corresponding 

 to UM time of the observation can be calculated. But the time at the 



observation, and hence the 

 de may be determined on 

 I used, with much greater 



accuracy than at tea. All ships and travellers ought to be well supplied 

 with chronometers, that is, the means of keeping their Greenwich time 



e me o e oservaton can e cacuate 

 place U alwayi supposed to be known from obs 

 dlffamtne gives the longitude. The longitude 

 hare by lunar observations, and, if a stand be 



B by observation they have got it, and then the result of the observa- 

 tion and computation b simply stated to be the error of the chronometer 

 on Greenwich time. The chronometer, if the rate be pretty well 

 known, continue* to give the Greenwich time (the correction for error 

 and rate being applied) for several days ; and the longitude is found 

 very day, by comparing the actual time at the place of observation 

 with the Greenwich time at the tame moment, given by the chrono- 

 meter. We have spoken as if one chronometer alone were used, but it 

 b mere folly to rely upon one or even two chronometers in a ship, or in 

 important geographical lesuaruhte * These are to be compared from 

 day to day, to ascertain that they are not suddenly altering their rates, 

 and also whenever any astronomical observation b made which .1, 1. 1 

 mine* UM Greenwich time (for that gives the error of each of tl,,- 

 chronometers), or the time at the pUoe. In reducing observed lunar 

 dieUnces to the true lunar distances, the altitude! of the mm and 

 mono, or noon and stars at the time of observation are required, and 

 at Ma two observer* are commonly set to measure these altitude! at 

 UM moment UM lunar observer gives a aignal that be hat made the 



la (a* in* plae* throaomtton an liable to Meidmta, and moodly, to 

 taeaf* Ihrir rat**, sad that Djaetha* by jump*. With two chronometer* erl. 

 tee* b (Km of error by their dlssnpaao*, and with tone, tut faulty ehrono. 

 tier Bay W detected. The btet two-day bos-ehronometn auy b* btm),t for 

 tatty (Bteeea, sad Ike be* fold awl *U**r poeaebehronometen (br forty sad 

 thirty o'*'" rnpeailTf ly. There U an Idle opinion that rbmnom. ter> are not 

 feed pceheuwauhra. They are pnbap* little awn liable to Injury rAm Itl 

 /*//, then ethei watch**, e* aemnt of the heavy eompruatcd balance, but 

 after weartaf tbrstwewtm tor year, without any particular care, we bcllcvr 

 UM three |td patket-eaceaaaMUn, Bet larfer than common watches, will 

 heep UM Uaw for a month, M*eUa*U**ab*c<*by lunar dUtancr. 



ronUct; indeed a fourth person it sometimes engaged in noting the 

 chronometer. On shore this profusion of aids cannot always be ol>- 

 tained. nor are they at all wanted. If the time at the place and the 

 latitude be known, the altitude! may be computed, or the observer 

 may proceed thus : 1st, an altitude of the sun, planet, or star ; -u.lly. 

 an altitude of the moon's bright limb ; Srdly, three lunar distances ; 

 4thly, a second altitude of the moon ; and Sthly, a second altit 

 the star or sun, noting the chronometer at each observation. II, will 

 then have the means, by simple proportion, of reducing the all 

 to what they would have been at the time of observing the lunar 



We ahould advise observers, who are properly furnished with chrono- 

 meters, rather to make a large number of observations on a few favour- 

 able nights, than to take a few observations on many nights. By 

 observing several lunar distances on both sides of the moon, and from 

 all the stars and planets east and west given in the ' Nautical Almanac/ 

 the errors of the instrument may be in a great measure eliminated, 

 and the error of observation much diminished. It in evident tint it 

 two equal distances are taken, one east of the moon and the other west, 

 then any error of the instrument, such as erroneous index error, v..mt 

 i>f parallelism in the glasses or telescope, exccutricity, &c., would be 

 the game in each, and therefore could be got rid of. In liku manner, 

 if two observations on the same side of the moon give different longi- 

 tudes, it is clear that the instrument haa some error which is nut in,lrx 

 error. On this subject we shall have occasion to speak again in treating 

 of the sextant. The luni-solar observations are generally preferred by 

 seamen (and they are perhaps the most satisfactory), partly perhaps 

 became the altitude of the sun, by giving time at the place, is imnii- 

 diately applicable to the determination of the longitude. The longi- 

 tude from lunar distances, however carefully taken, cannot be relied 

 upon to very great nicety. With all appliances, a distance to 10", and 

 a longitude to 20*, or ( ',tli of a degree, can scarcely be considered as 

 certain, and the errors of the lunar tables will not uufruquently duuMe 

 this error. At sea it would not be safe to rely on any n-i 

 lunar distances for a less quantity than 1" of longitude, or 4th of a 

 degree, but this is quite sufficient for the purposes of navigation in open 

 seas. 



The computation of lunar distances is very easily performs 1 I'.v 

 Thomson's tables, which are exceedingly convenient, and reijuhv only 

 a little more extension. They are approximate, but near enough, for 

 the navigator and the traveller en male. As the last accur.n 

 only be given to the computations after the errors of the lunar 

 are corrected, there is no need of much refinement in the previous 

 work. 



It has been proposed to determine the longitude on shore by biking 

 altitudes of the moon with the mercurial horizon ; and between ami 

 near the tropics the method may be a good one. In these low lot 

 the motion of the moon in altitude is nearly vertical and very 

 and this motion U doubled by observing the distance between the 

 and its image seen by reflection. The bright edge of the moon is a 

 good object in reflecting instruments. The calculation may be made 

 thus : The time at the place must be most scrupulously determined, 

 and the error and rate of the chronometer known, if possible, by equal 

 altitudes of the sun on each side of noon and midnight. Tlu-n. 

 the error of the chronometer being known at the place and time of 

 observation, assume an approximate value of the longitude, and deter- 

 mine the Greenwich time, the R. A. and declination of the moon, and 

 ita apparent diameter and parallax. Each altitude of the moon will, 

 when properly reduced, give an error of the chronometer, wliich, it" the 

 assumed longitude be correct, will agree with the error obtained by the 

 sun or stars. If there be a difference, a second longitude may bo 

 assumed, and thus, as has been shown in speaking of transits oi the 

 moon, the terms may be obtained from which, by a f<imi,lf ]>ro] 

 the true longitude can be deduced. It is not improbable that the 

 doubling the motion of the moon in observing by reflection, and the 

 sharpnoss of the images, may make up for the error committed in 

 ascertaining and keeping the time; but of this the observer must 

 be the judge. 



mimaiim of Greenwich Time by Chronometers. Hitherto the 

 Greenwich time hat been extracted from astronomical phenomena, but 

 where the distance is not great, the time may be brought from (ireen- 

 wi,-li by chronometers. Suppose, for instance, the longitude of Madeira 

 were required : then, having ascertained the errors and rates of several 

 good chronometers at Greenwich, they are carried to Madeira, and their 

 errors on the meridian of Madeira, and their rates, determined there. 

 The Greenwich time is known from each chronometer, supposing the 

 rate during the voyage to be the mean of the rates before and after, 

 am) t IUIK each chronometer gives a longitude of Madeira, and the mean 

 of the whole is taken. The voyage back to Greenwich, in like n, 

 with the errors and rates on arriving at Greenwich, furnish a second 

 longitude; and if the motion at sea has any tendency to alter the rates, 

 this cause will affect the first determination with a certain error, while 

 it aflects the second determination with exactly the same error, but in 

 nt sense. If it increases the difference of longitude one way, 

 it <l;iniiiinhe<i it the other way. By a mean of several such voyages the 

 dUhrvnot ,-f longitude of place* within a week or perhaps a fortnight's 

 j'nini-y may be ascertained with considerable exactness. There arc 

 some precautions to be adopted iu determining longitudes eluono- 



