1 68 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



divide by the interval of time /, / , and thus find the local acceleration at the epoch 

 k+(*i~~0- Then the sum of the two partial accelerations will give the best value 

 of the acceleration at this epoch. 



As even the determination of stationary acceleration involves a vector-addition, 

 the complete determination of the field of acceleration will involve the performance 

 of no less than two vector-additions and one vector-subtraction. The work will 

 therefore continue laborious. But as this kinematic determination of accelerations 

 will never enter as a link in the chain of operations which must be performed for the 

 solution of the problem of prognosis, a practical demand for special rapid methods 

 will not be required. 



199. Return to the Problem of Prognosis. It may be useful to consider a little 

 more closely what could be done for the problem of prognosis as soon as we can 

 determine by dynamic methods the accelerations of the moving particles. 



To the displacement AB' (fig. 113) found in the first approximation we should 

 then be able to add the displacement B'B due to the acceleration. In this manner 

 we should be able to forecast the displacements of the particles with a higher degree 

 of approximation, retaining the length of time for which we make the forecast; and, 

 dispensing with the greater accuracy, we could make the forecasts for longer periods. 



But in addition to this we should also be able to prognosticate the new field 

 of motion. For we know the velocities which the particles have when they arrive 

 at their new positions, and we can then draw the field of these velocities. Instead 

 of this discontinuous method we could also use a continuous one. From the field of 

 velocities observed we should have to derive that of stationary acceleration. Sub- 

 tracting this field from that of the true accelerations, which we calculated by dynamic 

 methods, we will get the field of local acceleration. Multiplying this by a suitable 

 interval of time /, / , and adding to the field of velocity at the time t , we get the 

 field of velocity at the time /,. Thus, as soon as the dynamic method has given us 

 the field of accelerations, kinematic methods, which we have treated already, allow 

 us to determine the future field of horizontal motion. From this we may again, by 

 kinematic methods which we have developed, derive the correlated vertical motions. 



