I30 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



between them can be very well illustrated in connection with the different methods 

 of observing the meteorological elements. The instruments of the ordinary meteoro- 

 logical stations give the local variation of the meteorological elements. When we 

 determine from the records of the barograph the rise of pressure per second, we get 



the local derivative of the pressure, c -- . In the same manner the thermograph 



ct 



of the station will give the local derivative of temperature . By use of the wind- 

 fane and the anemometer of the stations we can in the same way determine the 

 local time-derivative of velocity . We may call this the local acceleration, to 



ct 



distinguish it carefully from the acceleration without further specification, which 

 gives the rate of change of velocity of one and the same moving individuum. 



Instead of considering the stationary instruments of a common station, we can 

 now consider the moving instruments in a balloon, and let the balloon be in perfect 

 equilibrium. It will then move along within one and the same mass of air. The 

 barograph will then register the pressure of this mass of air, the thermograph will 

 register its temperature. Forming from the records the rates of change, we get the 



individual time-derivatives -?-> -^ . . . . If finally the velocity v of the balloon 



dt dt J 



itself be registered, we should be able to determine the acceleration of the mass 



of air in which it moves. 



At the moment when this balloon with its moving instruments passes the 

 station with its stationary instruments, the moving and the stationary instruments 

 will show the same instantaneous values of the recorded quantities, but different 

 rates of their change. Formula (d) will give the relation between the derivatives 

 found from the records of the moving and the stationary instruments. 



