ELEMENTARY PRINCIPLES OP KINEMATICS OF CONTINUOUS MEDIA. 3 1 



change of pressure of one m-bar per hour will have smaller effect than the change of 

 temperature of one degree centigrade per hour. Now the change of pressure of a 

 few m-bars per hour for columns of air of this length will have about the same 

 degree of probability as the change of temperature of a corresponding number of 

 degrees. Thus we have an equal right to neglect the influence of local pressure- 

 changes as of local temperature-changes. 



When we determine vertical velocities in the atmosphere by the condition of 

 the solenoidal nature of specific momentum, we may thus get errors amounting to a 

 few millimeters per second at the height of 1000 meters and of a few centimeters per 

 second at the height of cirrus. As the errors due to the uncertainty and the incom- 

 pleteness of the observations of the horizontal velocities will be much greater, these 

 errors must be considered as insignificant. 



We can therefore set down as fundamental principles to be used in the diagnostic 

 work regarding the fields of motion in atmosphere and hydrosphere: 



(A) In hydrosphere both velocity and specific momentum fulfil the solenoidal 

 condition. 



(B) In atmosphere specific momentum fulfils the solenoidal condition. 



Finally we have, independent of every approximation: 



(C) At every surface velocity fulfils the solenoidal surface-condition. 

 As a special case of this condition we have 



(D) Both velocity and specific momentum are tangential to every resting 

 boundary. 



