GEOGRAPHICAL LATITUDE. 775 



was brought to bear also on this subject, aud though starting with an 

 entirely different hypothesis, their results were both quite accurate. 

 The former, believing light to be a material substance, supposed that 

 the heavier medium attracted more powerfully and thus produced re- 

 fraction ; the latter, having proposed the wave theory of light, taught 

 that it is more difficult for the waves to force their way through a dense 

 medium than through one less dense; that their motion is thereby re- 

 tarded, and when striking the denser medium at an oblique angle that 

 their direction is changed. 



The earliest astronomers who considered the subject supposed the 

 atmosphere of the same density everywhere, and hence presumed that 

 the light-ray was only bent once and formed a straight path through 

 the air ; but from the time of Newton and Huyghens this idea was 

 shown to be untenable and that the path is really a curve. What the 

 exact nature of this curve is it is extremely difficult to determine, on 

 account of the presence of a large number of possible disturbing ele- 

 ments. With the gradual increase of accuracy, the older tables of 

 Cassini, Bradley, Berg, and Burckhardt and others have given way, 

 one after the other, to ever newly appearing ones. The present ones of 

 Laplace, Bessel, Schmidt, and Ivory are models of accuracy and fully 

 answer the needs for furnishing the amount of refraction in all cases.^ 



Progress of determining the latitude of fixed points. — At the renais- 

 sance of geography, almost the entire political fiice of Europe was found 

 changed from what it had been when Ptolemy's work was written. In 

 that work but few latitudes had been given, and these were generally 

 seriously lacking in exactness. The Arabs had added considerable 

 thereto, but in the region foreign to those with whom the advancement of 

 the science now rested. At first the modern geographers dared not dis- 

 pute the authority of the great master, and the first to print a map with 

 corrections offered therewith excuses for breaking with the tradition. 

 The need of accurately fixing latitudes was soon felt. The gnomon was 

 revived and made larger and better. Even as late as the elder Cassini, 

 a gnomon of 20 feet in height was used to determine the latitude of 

 Bologna ; ^ and still later (1744) Lemonuier added to his gnomon a burn- 

 ing glass of three inches diameter aud 80-foot focus, by means of which 

 latitude could be as accurately determined as by the great quadrants 

 of the time.^ But the days of gnomons were numbered, aud the newer 

 instruments took precedence. There followed a general improvement in 

 the determination of latitude by observation, a few examples of which 

 may be of use to show the rate of progress. 



Stirveys. — In the history of geographical latitude the most conspic- 

 uous role has been played by the surveys which have been made to 



'Bruhns, 181. 



^Casaiui, Grandeur de la terre, p. 375. 



sDelambre, Astron. du xvili"'* si^cle, 180. 



