and on Astronomical Refractions. 471 



T = ^1^240] _ ^ 

 ;/+ 1-5112 

 Height in miles = [1-7506111] log (1 - Hq). 



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, 



l- r 



= -2, 



g' = #3 c ~ W- f c_M - ! + H f- See vol. xvi. p. 440. 



If 1- = 1 - CO 



'-■-it- 



-3 



2 k 



2(1 -i7)<r' M + (1 - Hfc 



■} 



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 



