﻿On the Determination of the Height of the Atmosphere. 353 



ceived. The faculty of accommodation possessed by the eye ac- 

 counts for this power of seeing distinctly through lenses differ- 

 ing slightly in focal length. 



The principle of a concave air-lens in an aqueous medium 

 can be applied to the construction of object-glasses of micro- 

 scopes for examining objects in water. For this purpose it is 

 best to imitate the construction of the object-glasses of ordinary 

 microscopes, and make the lower surface of the air-lens plane 

 while the upper is concave. There is hardly a limit to the inag- 

 nifying-power of such glasses ; but I do not suppose that a lens 

 of greater power than \ of an inch focus will be required ; and 

 probably one of \ an inch focus, or even lower power, will suf- 

 fice for what I believe they will chiefly be used for, namely the 

 observation of the operations and organs of minute aquatic or- 

 ganisms. 



XLVI. On the Determination of the Height of the Atmosphere. 

 By Maxwell Hall, of Pembroke College, Cambridge*. 



LET p and p be the pressure and density of the air at any 

 point above the surface of the earth ; let g be the force of 

 gravity at this point, and r its distance from the centre of the 

 earth. Let p , p , g , and r be their values at the point on the 

 earth's surface vertically below the former, and let z be the dis- 

 tance between these two points. 



Suppose for the present that the temperature is 0° C. through- 

 out the atmosphere, and neglect the effect of moisture and of the 

 increase of the centrifugal force due to z ; then, if in the equa- 



tions p = kp(\+at), (1) 



%—» ^ 



9=3°(}+ S i) % (») 



we put t = 0, and k = ag , we shall get by integration 



i Po z 

 a log — = , 



** 1 + f? 



r o 

 or, approximately, 



'<•-;('- 9- « 



whence 



P- =€ -7X}-Q (5) 



Po " , 



* Communicated by the Author. 



