1 66 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



(after division by the square of the interval of time) the intensity of the acceleration. 

 When we have constructed this vector at a sufficient number of points, we can 

 afterwards draw its vector-lines or its isogons and its intensity- curves. 



197. Continuous Method for Constructing Charts of Acceleration. We can base 

 a continuous method of constructing accelerations upon the analytical representation 

 of this vector as a complex time-derivative and space-derivative. By formula / 

 of section 1 77 we have 



dv dv , 



H = * +vvv 



We have already called the first term of the second member the local accelera- 

 tion. If this term be zero 



9v 



Jt= 

 the wind-fanes of each station will show invariable direction and the anemome- 

 ters invariable intensity of the wind. The velocity-chart will remain unchanged 

 as long as this condition is fulfilled. The particles of air will then move along a 

 system of lines of flow which remain unchanged. The lines of flow will be the paths 

 of the moving particles. During this motion the particles will accelerate or retard 

 so as to take at every place precisely the velocity which is characteristic of the place. 

 We shall call a motion which is defined by this condition a stationary motion. The 

 acceleration which the particles of air must have in the case of stationary motion 

 is obtained if we set the local acceleration equal to zero in equation (/) of section 

 177; i. e., the term v V v represents the acceleration which the particles must have 

 if the motion is stationary. 



We can therefore state : The acceleration of the moving particles may be rep- 

 resented as the vector-sum of two partial accelerations : 



(A) Stationary acceleration which is given by the space-derivative 

 (a) vVv 



(B) Local acceleration which is given by the time-derivative 



< '5 



We have already treated the construction of fields representing derivatives 

 of the forms (a) and (b) . We can thus construct the fields of the two partial accel- 

 erations, and form their vector-sum 



(C) It " * + VVV 



which will then give the field of the true acceleration. 



(A) Stationary acceleration. When a velocity-field is given, the field of sta- 

 tionary acceleration (a) can be found in the following way (see section 174). 



(1) We perform the derivation of the half square of velocity with respect to 

 the lines of flow, i. e., we form the field 



