CHAPTER XII. 



KINEMATIC PROGNOSIS. 



190. Determination of Displacements from Given Velocities. The fundamental 

 kinematic vector, velocity, is by its very definition a quantity of prognostic nature. 

 If the initial position and simultaneously the velocity of a particle is given, it will 

 always be possible to make a certain definite statement regarding its future position. 

 How far in the future this statement will have any value will depend upon the 

 time-variations of velocity. If it does not vary, either in direction or in intensity, 

 the determination can be made for any future time. But if the velocity varies 

 according to an unknown law, the forecast will be of value only for a limited period 

 of time. When we select a sufficiently short period, the variation of velocity will 

 have insignificant influence, and the prognosis of the future position can be based 

 exclusively upon the knowledge of the initial position of the particle and the initial 

 value of its velocity. 



This kinematic prognosis will always be the first step when a rational precal- 

 culation of future atmospheric or hydrospheric states is to be made. In principle 

 this step will be perfectly simple. The only delicate point will be the choice of 

 proper periods for which the prognosis may be ventured. They can only be found 

 by experience. As regards the case of the hydrosphere our experience is still quite 

 insufficient. As we have not been able to produce any example of kinematic diag- 

 nosis, we can not give any of kinematic prognosis either. As regards the atmosphere, 

 our preliminary experience seems to indicate that periods of a few hours may be 

 used, say from one to six hours. If three hours are used, this period will be con- 

 venient also because it is in rough approximation a decimal multiple of our unit of 

 time, the second, viz, 10,800 seconds, or in the mentioned rough approximation 

 1 0,000 seconds. 



191. Synoptical Representation of Horizontal Displacements. When a chart 

 of horizontal velocity is given, the tangent to a line of flow gives the direction in 

 which the displacement of any particle takes place, and the scalar value of velocity 

 multiplied by 10,800 gives the length of the displacement in three hours. On the 

 velocity-chart we can thus easily mark the initial and the final situation of any 

 number of points, marking, for instance, the initial position by a little circle with a 

 dark area, and the final position with a corresponding circle with a white area. 

 In order to show which points belong to each other we can draw a line from each 

 black circle to the corresponding white one. 



In order to make conspicuous the chart of horizontal displacements, it will be 

 advantageous to choose systematically the initial situations of the points. They can 

 be chosen so that they belong to a set of isogons, or so that they belong to a set of 



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