556 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



The deduction of the amount of the available kinetic energy for 

 the whole system is rigorous as there given, but is inaccurate in the 

 present article. The mass of air does not remain at rest when m 

 moves through it; also, even if the energy of every particle of the 

 mass is small, still the sum total may be of the same order of mag- 

 nitude as the kinetic energy of m. 



With this proviso I will quote some figures computed by these 

 last equations in order to show how large the velocity may be that 

 is produced by this force of buoyancy when the initial difference of 

 temperature amounts to io°. 



When the acceleration is o the greatest absolute value of the 

 velocity iv will be attained at the altitude £, where 6 = T. Let the 

 temperature of the larger mass of atmosphere at the initial position 

 z be T = 2 73 C. and in general T = T — a (z — z ) ; when a = 



ST , . 



— = o we obtain 

 dz 



rfor O = r + 10°, C-~o= 988.6 meters, iv = 18.8 m. /sec. 



\for O = T - 10°, £-z --1025 meters, w = -19.3 m./sec. 

 Therefore the values of £ — z and w are larger in proportion as the 

 rate of vertical diminution of temperature throughout the mass of 



g dT 



atmosphere is larger; thus when a = £pr = ^r^ we have 



r for O = T + 10°, C _ ^o= 1942 meters, w= 26.4 m./sec. 



\for 6 Q = T - 10°, £-s = - 2090 meters, w— -27.4 m./sec. 



Similar computations for moist air are given by Reye in his "Wirbel 

 sturrne" Hanover, 1872, p. 227, etc. 



§(20) Computation of J Tdm for linear vertical diminution of 

 temperature in the column of atmosphere. 



Assuming T = T — az then for the state of rest [or hydrostatic 

 equilibrium] the pressure is given by the integration of the equa- 

 tion (a), i. e., 



T \o/Ra 



P-Po 



whence we deduce the following equation (3), that will often be 

 used hereafter, for the integral of the product of the temperature by 



