ON THE ENERGY OF STORMS — MARGULES 537 



where dp is the change in the potential energy of position for the 

 whole system including that of the piston, dp and 0/ are the anal- 

 logs of the exterior work and the change of internal energy of a 

 small mass of air under constant pressure. These equations hold 

 good in general for any change of location of the masses of air when 

 the pressure remains constant in the superposed movable level 

 surface. 3 The integrals are to be extended over all the masses 

 lying below this surface. 



The quotient of the available kinetic energy by the mass below 

 the piston gives the average energy £V 2 per unit of mass. When the 

 above assumed overturning of the masses takes place and the 

 volumes of the two chambers are equal, the corresponding value of 

 V is given by 



V = £V7¥t~ 



where g — acceleration of gravity; h = altitude of the chambers; 

 7\ and T 2 are the initial average temperatures: t = (T 2 — T,)/7\. 

 Assuming 7\ = 273 , T 2 = 283 and h = 2000, 3000, 6000 meters 

 successively, we find V = 13, 16, 23 meters per second respectively. 



In the case of cold and warm rooms in dwellings having the same 

 temperatures as above but h = 5 meters we find V = 0.67 m./sec. 



But this computation tells us nothing as to how the available 

 kinetic energy is distributed within the masses. We see, however, 

 that with chambers 2000 meters high and a difference of tempera- 

 ture of io° C. a storm velocity cannot prevail throughout the 

 whole mass but only in about one-fourth part of it, and in even a 

 still smaller fraction of the whole mass if we abstract a large amount 

 for the loss of the energy due to friction. In boe-en or gusts, strong 

 winds occur only on the cold side and close to the boundary. 4 



The ratio of R to C v is that of 1 to 2.5 and by this ratio is the 

 work done by the force of gravity less than the diminution of 

 internal energy when the change of location takes place under con- 

 stant pressure. When the overturning takes place under constant 

 volume we have the same value of V, and so also when it takes place 

 with a very slow change of pressure in the level surfaces near the 

 boundary; but in these cases the ratio dp/dl is changed. We 

 have the same available kinetic energy if we fill each chamber with 

 an incompressible fluid whose mass is the same as that of the air 

 in this chamber, but in this case the energy arises from the work 

 of gravity only. 



3 Corresponding to the piston. 



4 So also in northers, blizzards, chinooks, boras, purgas, etc. — C. A 



