357 



LONGITUDE AND LATITUDE. 



LONGITUDE AND LATITUDE. 



858 



the prize held out by the legislature. Some persons still occupy them- 

 selves in this manner ; and it is impossible to persuade them either of 

 the repeal of the Acts of Parliament, or of their having mistaken the 

 nature of the difficulty, which is now, for all practical purposes, 

 entirely conquered. It is impossible to find the latitude of a place 

 without knowing the position of the equator in the heavens, or the 

 longitude without knowing the meridian of Greenwich. The equator 

 has a real existence in the heavens, since its pole is the immovable point 

 of the heavens, which can be detected (though it is not absolutely 

 occupied by a star) from observation of the motion of the stars, which 

 always preserve their distance from the pole. But the meridian o 

 Greenwich, a purely arbitrary circle of the earth, determined mereli 

 by the will of Charles II., that an observatory should be built on a 

 certain hill near London, has no representative in the heavens. The 

 only method, then, of finding longitude of the heavenly bodies is by 

 finding the hour of the day which it is at Greenwich, at a particulai 

 hour on the spot whose longitude is required. It is then known how 

 much of 360 degrees is revolved -through by the earth in. the period 

 which brings a star from the meridian of the place upon the meridian 

 of Greenwich, or rice rend ; and this angle is the longitude. A watch 

 which goes correctly and is set at Greenwich will carry the time a1 

 that place all over the world ; or a celestial phenomenon, of which the 

 Greenwich time may be predicted, will, if the moment of its happening 

 be observed at any other place, give the difference of times at the 

 moment of observation. Any proposal for finding the longitude astro- 

 'illy, which does not depend on one or the other of these prin- 

 ciples, is useless, unless it be that of actually measuring the distance 

 between the given place and Greenwich, the latitudes of both being 

 known. Whether it be possible to use any other than astronomical 

 means for the purpose, it would be presumptuous to decide ; but there 

 certainly is no other method which offers the most distant prospect of 

 (success. 



LONGITUDE AND LATITUDE, METHODS OF FINDING. 

 We shall classify the various modes of determining geographical lati- 

 tude and longitude, partly by the instrumental means of the observer 

 .-I] i<l partly by the nature of the phenomena. The problems are of 

 < the same whatever instrument is employed, for the latitude of 

 a place is the altitude of the pole of the heavens at that place, and the 

 longitude is the difference between the time on the first meridian (we 

 shall always suppose Greenwich to be the first meridian) and the time 

 at the place, at the same physical instant. 



Determination of the Latitude at FUed Observatories and Inde- 

 pendently. 1. In determining the latitude at fixed observatories which 

 are furnished with accurate circles, mural, transit, or altitude and 

 azimuth circles [CIRCLE], the altitudes or zenith distances of circum- 

 .stars are observed above and below the pole. When the.se are 

 i-ly reduced, the place of the pole (which lies between the places 

 of upper and lower culmination of each star) is known, and hence the 

 latitude is found. The first object of all astronomers is to fix the 

 latitude of their place of observation, and the details of this operation 

 will be found _in the beginning of most of the published series of 

 observations. The account of the latitude of Greenwich in the Green- 

 wich Observations for 1836, p. Iviii., of Cambridge in the Observations 

 of 1833-4-5, and of Edinburgh, 1834-5, may be consulted by those who 

 wish to know what the process is, with the most perfect means which 

 we at present possess. 



2. Again, if the altitudes or zenith distances of the sun be observed 

 several days before and after the summer and winter solstices, the 

 altitude or zenith distance of the middle point, that is, of the equator, 

 may be deduced. Since the tables of refraction have been perfected by 

 Bessel, these observations give a satisfactory latitude. Both methods 

 may be considered to be independent, as they do not draw their data 

 from other observatories, and no great accuracy is required in the 

 solar tables to reduce the observations of the sun to the solstice. 



'. Lat, Greenwich Observations,' part v.) 



In the observatories of Europe, and generally where the visible pole 

 of the heavens is tolerably high, the latitude is best determined by 

 circumpolar stars ; near the equator an independent latitude must be 

 'ed from circumsolstitial observations. 



3. Before the introduction of circles, the latitude in fixed observa- 

 tories was derived from combining two instruments, the mural QUA mt A NT 

 and the ZL-.MTH SECTOR. The zenith distances of stars near the zenith, 

 and to the north or south of it, were observed by the zenith sector, 

 and al-io the distances of the same stars from the pole or the equator 

 by the quadrants ; hence the arc between the pole and zenith (the co- 

 hititude), or between the zenith and equator (the Latitude), was deduced. 

 The place of the pole was found on the north quadrant from circum- 



tars, and the place of the equator on the south quadrant, from 

 observations of the sun near the solstices, as we have described above. 



. 



tiw preMDi / nith tube was erected at Greenwich, one of its 

 intended uses was to perform the same office for the mural circle as the 



al zenith sector did for the quadrants. 



I'ei" ' '! Differentially. 1. The ZENITH SKCTOR, 



when of the proper size and construction, is perhaps the most accurate 



.ment for determining latitudes diferentialli/, that is, assuming 



liicli are cither known or can be obtained from fixed observa- 



With this instrument, the meridian zenith distances of several 



stars which pass near the zenith may be observed with great certainty ; 



and as the polar distances of those stars are or may be determined at 

 first-rate observatories, the polar distance of the zenith, or the co- 

 latitude, is known. The latitudes for the trigonometrical survey of 

 Great Britain are thus deduced by comparison with Greenwich, the 

 instrument employed being a very fine 8-feet zenith sector by Ramsden. 

 With a better knowledge of the proper motion of the stars, the sector 

 might be used at two places, and the arc between those places obtained 

 from observations of the same stars at two epochs, without reference 

 to any other observations ; but at present it is safer, when practicable, 

 to refer directly to corresponding observations made at a fixed 

 observatory. 



2. Another differential method has lately been much used (at least 

 by continental astronomers), in which the transit instrument alone is 



employed. [TRANSIT.] The axis of the instrument is placed north 

 and south, and carefully levelled, in which case its line of sight will 

 describe the prime vertical. In the figure, let p be the place of the 

 pole, x the zenith, EZW the prime vertical, which is also the line 

 described by the middle wire of the telescope when it revolves. Let a 

 star, of which the polar distance is well known, be observed at s and 

 s', and the times noted. Then P s, the polar distance of the star, is 

 known, and the angle s p s' is equal to the time between the observa- 

 tions, and consequently s p s', or s p '/., is known ; hence we have s p 

 and urn in the right-angled spherical triangle s p z, and tan p z = tan 

 P s x cos / s P z, from which p z, or the co-latitude, is obtained. This 

 is perhaps the most accurate mode of determining the latitude with 

 moderate instrumental means. The transit should be reversed on 

 alternate nights, so as to get rid of the effect of imperfect collimation 

 or unequal pivots, and the level applied repeatedly before and after the 

 observations. The method depends mainly upon the delicacy of the 

 level and the perfect truth of form in the pivots, and when all precau- 

 tions are taken the results are surprisingly good. The supports of the 

 instrument must also be perfectly steady during the levelling and the 

 observation. Differences of latitude may be determined by the transit 

 instrument independently, by observing the samo stars at the two 

 stations. In this case any error in the assumed polar distance of the 

 stars will not affect the accuracy of the result. 



3. If an observer can carry with him a circle, either an altitude and 

 azimuth, or a repeating circle, he may determine the latitude by cir- 

 cumpolar stars independently : but it is better to observe the zenith 

 distances of well known stars several minutes before and after they 

 >ass the meridian." [CIRCLE; REPEATING CIRCLE.] The reduction 

 ;o the meridian is. easily computed [REPEATING CHICLE], and the places 

 of the stars inserted in the ' Nautical Almanac ' are sufficiently accu- 

 ate. It is advisable to observe stirs at different zenith distances from 

 70 on each side, to near the zenith, because if there be any fault in the 

 instrument which depends on the zenith distance, the stars will be 

 affected similarly on both sides of the zenith, that is, the zenith 

 distances to the north and south will both be too large or too small, 

 ^fow as the co-latitude is equal to the zenith distance ^ the polar 

 distance when the star is north of the zenith ( + when observed above 

 ;he pole and when observed below) and is equal to the polar distance 

 zenith distance when the star is south of the zenith, it is clear that 

 an error in the zenith distance will have precisely opposite effects on 

 .he co-latitude deduced from a north and from a south star. Besides, 

 he coincidence or discrepancy of the observations will afford a tolerable 

 notion of the instrument and the observer, and of the value of the 

 inal result. The repeating circle was at one time over estimated, and 

 >erhap3 at present is not quite rated at its true worth. A careful and 

 ntelligenf observer will come Very near the truth with it, or with the 

 altitude and azimuth circle. Both are rather troublesome to use, and 

 roth require either a very solid support, or a second observer to read 

 he level while the first observer bisects the star and notes the time. 

 s T either can they be considered as portable in ordinary circumstances, 

 when large enough for convenient use. The altitude circle should 

 scarcely be less than 1 2 inches in diameter in either construction. On 

 ,he whole we are inclined to prefer the repeating circle as a travelling 

 nstrument, and the altitude and azimuth for a permanent situation 



The number of minutes which it will be prudent to observe depends on 

 everal circumstances. If the time is known to one eecond, which it ought to 

 je, the observations may be commenced whrn an error of I" in the time will 

 ffect the latitude 1". In ordinary case.*, and for observers who do not uniltr. 

 land the reason of the thing, 10" on each side of the meridian is a sufficient 

 lirection. 



