and on Astronomical Refractions. 



- 448'. 



4-71 



p + 1-5112 

 Height in miles = [1-7506111] log (1 H q}. 



Mr. Russell has calculated for me the following table in order to 

 show in what manner the density and temperature of the atmo- 

 sphere vary in the higher regions under these three different sup- 

 positions. 



By making y= 1-5, the expression for the density becomes 



simplified, = 2, 



1 v 



1 + H > . See vol. xvi. p. 44-0. 



If i- = 1 - , 



* 



.-3u 



It must be recollected that the difficulty of determining the den- 

 sities at different altitudes, and that of determining altitudes by ob- 

 servations of the barometer, rest in finding the accurate law of the 

 temperature. So that if the expression which I have here suggested 

 for the temperature be adopted, the expression for the density, and 

 those for finding the elevation by observations of the barometer, 

 follow as a matter of course, and their accuracy is unquestionable. 



The employment of the formula in p. 467, for calculating heights, 

 amounts to determining the constant E from the observations 

 themselves, and not from previous observations. But if the 

 constants are supposed to be known, as in calculating a series of 

 observations made under the same circumstances, it is more simple 

 to employ the expression 



