538 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



§(4) Let us now consider another system. In the chambers (1) 

 and (2) of fig. in let two masses of air be enclosed whose respective 

 entropies are the same at the same altitudes: therefore the greater 

 pressure will be on the side of the warmer air; a difference of pressure 

 of io mm mercury at the base implies a difference of temperature 

 of i°C. only. Let each of the two masses be initially in stable 

 equilibrium. 



If now the screen be removed and the total volume be unchanged 

 then the horizontal strata that were initially at the same altitudes 

 unite to form one new stratum. The vertical succession remains 

 unchanged and so also the altitude of the center of gravity. The 

 change of internal energy as computed for the unit of mass depends 

 only on the initial difference of pressure, not on the height of the 

 chambers. We may therefore replace this system by a thin hori- 

 zontal stratum that initially contained air in two equal divisions 

 at pressures of 765 mm and 7 55 mm mercury respectively. The 

 available kinetic energy is that appropriate to a velocity of 1.5 m/sec. 

 for the whole mass: that which is available for each unit of mass is 

 far smaller than in those systems that with the same distribution 

 of pressure at the base have horizontal differences of entropy. 



It has already been shown by me, in my treatise, ''On the work 

 represented by any distribution of atmospheric pressure" 5 that 

 the energy stored up in such a distribution of pressure as is 

 observed in our lower strata during a stormy period would not suffice 

 to develop the observed kinetic energy of the storm, if the masses 

 of air were only pushed horizontally out of their positions of equilib- 

 rium. 



A great velocity of a mass of air over a broad area under the 

 influence of a horizontal pressure gradient can only arise when 

 this gradient is maintained by some outside source of energy; 

 otherwise it would disappear before any portion of the mass of air 

 had attained the velocity of a moderate wind. Dry air possesses 

 such a store of energy when horizontal differences of entropy of 

 ordinary amount exist at any level; and not only when there is a 

 sharp boundary between warm and cold air but also when there is 

 a steady continuous horizontal gradient of entropy. 



§(5) The available kinetic energy of a system in which masses of 

 unequal entropy are superposed in unstable equilibrium can be 

 computed from the energy equation. Here we find a store of 



'Jubilee volume of the Central Institute for Meteorology, p. 329, Denk 

 schriften, Imp. Acad. Science. Vol. XXIII. Vienna, 1901. See No. XXIII of 

 this collection of translations. 



