GEOGRAPHICAL LATITUDE. 771 



directly opposite to each other, by which method each counteracts the 

 possible error of the other.^ 



With the advance toward perfection of tbe instruments of observa- 

 tion has naturally gone hand in hand the progress in the accuracy 

 of the astronomical observations themselves. Though Hipparchus 

 was far ahead of his predecessors in tbe liind of instruments he used, 

 his observations were still liable to an error of half a degree.^ Lelewei 

 gives the latitude of several places according to two Arabian authors, 

 which vary in each case three (!) degrees or more.^ There is a long dif- 

 ference between this and Picard's results, whose observations., accord- 

 ing to his own statement, did not vary one from another more than five 

 seconds.* Somewhat more than a century later Delambre made about 

 twelve hundred observations to determine the position of one of his 

 stations, and found them accord to within half a second.* Another 

 series gave a variation of only one-third of a second,^ and still a third, 

 consisting of eighteen hundred observations, made by Delambre and 

 Mechain, showed a difference of but one-sixth of a second in the results 

 of the two observers.^ These are the achievements of the most careful 

 observations with the finest instruments. About the same time Bohneu- 

 erger, writing of ordinary observations with the mirror-sextant, gives, as 

 the greatest possible error in observing the altitude of the sun, 23.5 sec- 

 onds,^ a tremendous advance on classical and mediaeval results. How- 

 ever, all modern observers do not find the same happy agreement in 

 their observations as did Mechain and Delambre. Even at the begin- 

 ning of this century a complaint is made that the latitude of the best 

 astronomical observatories is scarcely within three to four seconds cer- 

 tainly fixed, while that of Paris had varied between 1667 and 1721 a 

 quarter of a minute,^ and that of Berlin still later varied a whole 

 minute, according to the observations of two astronomers.'" 



Tables of positions of stars. — Of great importance for the determina- 

 tion of latitude, are the tables giving the exact position of the sun and 

 stars. Hipparchus calculated the length of the longest day for each 

 degree of latitude and in so far used the sun's position for geographical 

 purposes. But it is in modern times that man has first felt the necessity 



' " Besonders bequeiu sind die von Pistor und Martin's erfuudeuen Reflexions- 

 kreise, bei denen der kleine Spiegel dureh ein Prisma ersetzt ist. Diese habea iiber- 

 diea den Vortheil, dasa man damit alle Winkel von 8'^ bis 180° messen kaun" (Brii- 

 mow, Astrou., p. 540). 



2 Delambre, Astron. ancienne, i, xii. 



3 Br. Ed., I, xlviii. 



^Picaid, Mesure de la terre, 22. 



* Delambre, Base du 8yst^.me, i, 77. 



^ Ibid., 72. 



' Delambre, Base du systfeme, i, 04. 



^Ortsbestimmung, 145. 



»Zach., Mon. Cor., April, 1804, p. 270. 



'"Ibid., p. 284. 



