518 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



(a.) Horizontal motion in a steady field of pressure 



When gravity is the only exterior force and the distribution of 

 pressure remains unchanged, the equations of condition for hori- 

 zontal movements are: 



dV n A d P n 

 — = and — = 



dt dt 



whence 



1 dG 2 _ _ 1 dp _ RT dp 



2 dt [i dt p dt' 



(a) Under isothermal conditions, therefore, the integral becomes 



- {CP - G 2 ) = RT log Po 

 2 p 



where G , p and G, p are associated sets of values. 



(b) For movements with adiabatic changes (see 16) we have the 

 equation 



dt p dt 



Here it should be noted that the second term with its negative 

 sign represents the work of the pressural forces on the unit mass 

 in unit time in a steady field, and for subsequent use we also note 

 that the whole work done on the unit mass in moving it from p to 

 p or from T to T is equal to 



C p (T - T) 



This is quite independent of whether the motion takes place with 

 or without friction. In the case of frictionless motion we have 

 therefore, 



i {<? - Gl) - C v (T - T) = C p T (l - ( Py /C *} 



(c) If (p a — p) is small relative to p then the preceding equations 

 (a) and (b) give alike the same approximate formula for the increase 



