772 GEOGRAPHICAL LATITUDE. 



of being able to tletermiue each day and even moment his latitude; and 

 with the occasion of the necessity, were iavented the means of meeting 

 it. Not only were new instruments of observation placed at the dis- 

 posal of astronomers and mariners, but tables of the daily positions of 

 sun, moon, and stars, have been worked out with ever-increasing ac- 

 curacy, so that what was once a matter of impossibility to the best in- 

 formed astronomer and mathematician, viz, to determine any day his 

 geographical position on the earth, is now an easy matter for any mar- 

 iner of fair education. Though such tables were constructed by the 

 Greeks and Arabs, we must look to the French astronomer. La Caille, 

 and the German, Tobias Mayer, for the first approach to accuracy in 

 this regard.^ The former, using alike the work of his predecessors and 

 his own numerous observations, constructed about the middle of the 

 last century a table of 397 stars, which receives the highest praise from 

 Delambre.^ Mayer took up the work where La Caille left it, and sim- 

 plified the mathematical formulae, receiving a prize from the English 

 government for the benefit therefrom to navigation. This work was 

 then collated with the observations of the astronomer royal of England 

 by the mathematician. Mason, whose name in America is so well known 

 in connection with the Mason and Dixon's line. The accuracy of the 

 tables was thereby increased to such an extent that Maskelyne ex- 

 pressed the belief that the greatest error would not surpass thirty sec- 

 onds. Later laborers in the same field have materially diminished even 

 this small margin of possible error.^ 



Refraction — Several causes united to make possible a degree of accu- 

 racy which for ages was held to be unattainable. Among the most po- 

 tent of these factors were the discovery by Bradley of the aberration of 

 light and the nutation of the earth's axis ; and the great progress made 

 in determining accurately the amount of refraction in connection with 

 astronomical observations. As the latter was a matter of slow develop- 

 ment, it may be advantageous to consider it somewhat more in detail. 

 Astronomical refraction has been defined as the amount which the rays 

 of light are bent from their entrance into the atmosphere to us.* The 

 first recorded notice taken of this phenomenon was about the time of 

 the Christian era, when Cleomedes, in his work Circularis Inspectio Me- 

 teorum, relates an account which he had received of an eclipse of the 

 moon taking place when both sun and moon were visible above the hor- 

 izon. Though disposed to doubt the truth of the story, he gives a pos- 

 sible explanation of the phenomenon in remarking: " Even as a ring in 

 a vessel will be raised visibly above the edge by water poured in, so 

 can the sun be seen by refraction when it is in reality still below the hor- 

 izon." ^ The fact of refraction was known to Ptolemy, and that its 



' Delambre, Astrou. dn xviii"i« siecle, viii. * Ibid., 717. 



^ Ibid., 515. ^Bruhus, Strahlenbrechung. 6. 



' Ibid., 634. 



