774 GEOGRAPHICAL LATITUDE. 



density of the air is proportional to the pressure resting upon it, and 

 the second, that established by Hawksbee's experiment in 1702, viz, 

 that the refracting power of the atmosphere is as its density.^ 



In order to render practical — for determining astronomical refrac- 

 tion — the knowledge gained by these various discoveries it was neces- 

 sary to have the means of arriving at the amount of pressure on the 

 great body of atmosphere through which the light comes to the 

 observer, and also of measuring the temperature of the atmosphere. 

 These means were provided just at the right time by the invention of 

 the thermometer by Drebbel in 1638, and its perfecting nearly a century 

 later by the labors of Fahrenheit and Eeaumur ; also by the (if possible) 

 still more valuable invention of the barometer by Torricelli in 1643. 

 Thus at the beginning of the eighteenth century we find all the means 

 at hand, by which the cause and amount of astronomical refraction were 

 to be determined with the greatest accuracy, supplying the last requisite 

 to the exact determination of geographical latitude. Halley, by his ob- 

 servations in 1714-'15, was led to the conclusion that the change of 

 refraction is proportional to the change in the height of the barometer,^ 

 which was for astronomical refraction only the confirmation of the law 

 already proved for terrestial refraction by Hawksbee, viz, that refraction 

 is proportional to the density of the atmosphere, while later in the cen- 

 tury Euler called attention to t'je fact that refraction is almost exactly 

 in the inverse ratio of the degrees of heat, when the star is not too near 

 the horizon.^ Thus a large body of facts h;id been gradually brought 

 together, which was then systematized, and thereby was made possible 

 the establishing of theories as to the action of light on its way through 

 the atmosphere. They in turn became the foundation for calculating 

 accurately the amount of refraction when the conditions of the observa- 

 tions were known. The details of the matter lie outside of the scope of 

 this article; but a few of the most important points are worthy of a 

 moment's attention. Though Keplfer brought his great talents to bear 

 on the subject he failed to add anything to its elucidation.* Tobias 

 Mayer (already mentioned) was the first to give a rule for calculating 

 the amount of refraction in connection with the variation of the barom- 

 eter and thermometer.^ Oriani in 1788 showed that the change of 

 density of the air is without influence on refraction from the zenith to 

 a distance of 70 degrees^ (though of course the regular increment of 

 density and refraction continues), and Laplace showed that the same 

 is true to 74 degrees,'' and in fact he takes no account of the variation 

 of density in his formula up to 80 degrees.^ This probably accounts for 

 the fact that some early tables were quite accurate up to that point, as 

 was the case with Kepler's.^ The genius of Newton and of Huyghens 



iBrubns, 40. ^ Ibid., 41. 



^Delanibre, Astrou. du xvni™« sibcle, 785, note by Mathieu. 



"Bmbus, 15. ^Ibid., 78. 



^ Ibid., 74. ■'Ibid.,ZG. 



Ubid., 119. Ubid., 19. 



