SHORT MEMOIRS ON METEOROLOGICAL SUBJECTS. 401 



can be deduced from the above given values of o, R, and J. Observa- 

 tions on the velocity of sound in the air give 



k = 1.40, or ^-^ = 3.5. 

 Inveresly, 



^^ = 0.2907 or 0.2857, 

 and with this we have 



'From Poisson's equation we can also directly, and therefore without 

 the assistance of the principles of the mechanicaltheory of heat, deduce 

 the expression for the diminution of heat with altitude given on page 

 24, and may therefore represent it as a simple function of the density or 

 the pressure of the strata of air at different altitudes. If we combine 



the equation 



h 



P' \T'J 



with the self-evident relation 



we obtain 



\vj ~ T' ' 

 and thence 



p' - KFJ - \8') • 

 If in the equation dp = d dh we substitute for dp the differential of 



P=P'(J)\ 



integrate, and consider that 



^8 y-i T 



we find 



T' k p 



(William Thomson on the Convective Equilibrium of Temperature in the 

 Atmosphere, Mem. Lit. and Phil. Soc. of Manchester, 3d series, vol. ii, 

 18G5, read January 21, 18G2.) 



In this equation, I^, 5', and j/ are the values of temperature, density, 

 and pressure that obtain at any moment in the initial stratum of air. 

 For the surface of the earth, 



p' = 10333 kilograms, 



5' = 1.293. p: 



26 s 



