LONGITUDE. 



moon over the meridian, and comparing it with the paffage 

 obferved in fome fixed obfervatory. A much greater accuracy 

 will be obtained by this method, if feveral fucceflive tranfita 

 of the moon be taken at either place of obfervation, as then 

 the motion of the moon in riglit afcenilon will be obtained 

 without the aid of calculation : but it will be requifitc to 

 attend to the equation of fecond differences, and even then 

 the irregularity of the moons motion in 24 hours is fo great, 

 that a very fenfible error may ftill remain uncorrefted. 



Several writers, in explaining this method, appear to have 

 fallen into a mifconceptioii of the fubjeft, by confounding 

 together the retardation of the moon in 24 hours, with the 

 real retardation obferved between two fucceilive tranfits, 

 and which latter fliould evidently be ufed in calculating the 

 proportional retardation correfponding to a given difference 

 in longitude. Suppofe, for inftance, for the fake of render, 

 ing the fubjeft as intelligible as poffiblc, that the motions of 

 the fun and moon were pcrfeftly uniform and in the equator, 

 and that they both paffed the meridian of Greenwich at mean 

 noon (which would, according to our fuppofition, be the 

 fame as apparent noon) ; fuppofe that the next day the 

 moon paffed the meridian of Greenwich at 1 ' after noon. 

 It is evident that the retardation would be one hour in 

 tiuenty-five hours. On the oppofitc meridian the moon will 

 pafs ato" 30', at which inftant it will be 12'' 30' mean lime at 

 Greenwich, or the half of 25 hours, this being the proportion 

 of time anfwering to a retardation of 30'. In genera', the at- 

 tention of the calculator ihould be direfted to finding the 

 mean time at Greenwich, and to compare with this the mean 

 time at the place of obfervation. The reader, who wifhes 

 to fee more on this particular method, may confult a paper 

 by Mr. Gavin Lowe in the 15th vol. of Tilloch's Philo- 

 ■ fophical Magazine. 



Hitherto we have fuppofed two obfervations made by two 

 obfervers, one at each place, whofe difference of longitude 

 with the other is to be determined ; but it is evident that 

 this is imprafticable in many cafes, and particularly in the 

 one of the greatell importance, namely, when the objeft is 

 to determine the longitude at fea. Here the mariner muft 

 be fupplied with one calculated or fuppofed obfervation, 

 inftead of one really obferved. The difficulty to be fur- 

 mounted in this cafe is extremely great : of the immenfe 

 number of methods more or lefs piaufible that have been 

 fuggefted, two only are in ufe at prefent, the one by the 

 means of a chronomter, already explained at great length 

 under that article ; the other the lunar method, which 

 has been gradually improved by the labour of fucceeding 

 aftronomers, from the time it was firll fuggeftd, many years 

 ago, to the prefent moment, when it is brought fo near per- 

 feftion, that no leafonable hope can be entertained of any 

 very confiderable improvement. 



The early navigators had no means of eftimating their 

 longitude but by the computed run of the (hip ; and the 

 dangers they incurred by tliis inaccurate method, were fuf- 

 ficient to convince every enHghtened government, particularly 

 of maritime ftates, of the importance of encouraging, to the 

 utmolt effort of human ingenuity, what could be direfted to 

 the improvement of this defeClive ilate of navigation. 



The early fpeciilations, of aftronomeis were of but little" 

 praftical utihty to the navigation of thofe times. In the 

 1 6th century, cclipfcs of the moon were ftrongly recom- 

 mended ; but they happened very feldom, and were too in- 

 accurately computed to be of any great ufe. Perhaps, 

 now and then, the approximate longitude of an almoil un- 

 known country, wht-re a mariner might accidentally be on 

 fliore, was computed by this method, but to determine the 

 place of a (hip it was perfe<JtIy inadequate. 



Phihp III. of Spain, in 1J98, offered an hundred thou- 

 fand crowns ; and the ftates of Holland, at the beginning of 



I of 



the feventeenth century, propofed a reward of thirty thou- 

 fand florins to the perfon who Ihould be fortunate enough 

 to folve this difficult and important problem. In 1635, 

 John Morin, profeffor of mathematics at Paris, propofed 

 a method of refolving it to cardinal Richelieu, extremely 

 fimilar to the lunar method now in ufe ; but it was rejefted 

 as of no praftical utihty : and indeed, at that period, neither 

 the lunar tables were of fufficient accuracy, nor the nautical 

 inftruments delicate enough to render the lunar method very 

 promifing. However, though the commiffioners, who were 

 appointed to examine this method, judged it infufficicnt, 

 on account of the imperfeftion of the lunar tables, cardinal 

 Mazarin, in 1645, procured for him a penfion of 2000 

 livres. 



Many attempts were founded on the theory of the mag- 

 netic variation ; but none of thefe fucceeded. It was the 

 general opinion of allronomers, that the moon's motion was 

 the moft promifing phenomenon to feleft ; but long after 

 the idea was firft fnggciled, neither lunar tables nor inftru- 

 ments were fufficiently exaft to render any method, founded 

 on thij theory, praftically ufeful. Still, however, there was 

 a rational hope that thefe difficiJties might be overcome. 



The firft perfon who recommended the inveftigation of 

 the longitude, from obferving the diftance between the moon 

 and fome ftar, is faid to have been John Werner, of Nu- 

 remberg, who printed his annotations on the firft book of 

 Ptolemy's Geography, in 1514: Peter Apian, profeffor of 

 mathematics at Ingolftadt, in 1524 ; Oronce Fine, of Bri- 

 an9on, about 1530; Gemma Fnfius, at Antwerp, in IJ30; 

 Nonius or Pedro Nunez, in 1560 ; and Kepler, in 1630; 

 all fuggeft and recommend the fame method. In 1675, 

 king Charles II. erefted the obfervatory at Greenwich, and 

 appointed Mr. Flamfteed his aftronomical obferver, with 

 this exprefs command, that he fhould apply himfelf with the 

 utmoft care and diligence to the rectifying the table of the 

 motions of the heavens, and the places of the fixed ftars, in 

 order to find out the fo much delired longitude at fea, for 

 perfefting the art _ of navigation. To the fidelity and in- 

 duftry with which Mr. Flamfteed executed his commiffion, 

 we are in a great meafure indebted for that curious theory 

 of the moon, which was afterwards formed by the immortal 

 Newton. This incomparable philofopher made the beft ufe 

 which human fagacity could make of the obfervations with 

 which he was furniftied ; but, as thefe were interrupted and 

 imperfeft, the difference of fir Ifaae's theory from the hea- 

 vens would fometimes amount at leaft to five minutes. Dr. 

 HaUey employed much time on this fubjert ; and a ftarry 

 zodiac was pubhftied under his direftion, containing all the 

 ftars to which the moon's appulfe can be obferved : but for 

 want of proper inlliruments and correft tables, he could not 

 proceed in making the neceffary obfervations. In a paper 

 on this fubjeft he expreffes his hope, that the inftrument juft 

 invented by Mr. Hadley might be applied to taking angles 

 at fea with the defired accuracy. (See Phil. Tranf. N" 42 1.) 

 This great aftronomer, and after him the abbe de la Caille, 

 and others, have reckoned the beft aftronomical method of 

 finding the longitude at fea, to be that wherein the diftance 

 of the moon from tlie fun, or from a ftar, is ufed ; for the 

 moon's daily mean motion being about thirteen degrees, 

 her hourly mean motion is about half a degree, or one mi- 

 nute of a degree in two minutes of time ; and fo an error of 

 one minute of a degree in pofition will produce an error of 

 two minutes in time, or half a degree in longitude : and if 

 by obfervation it is determined what part of her daily motion 

 the moon has run through during the interval between a 

 certain point of time under a known meridian, and the 

 inftant of time when the obfervations are made on her, 

 under an unknown meridian, then her daily motion at that 

 time will have, to the part thereof determined by obferva- 

 tion. 



