8 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



representations in spite of the extreme incompleteness of the observations. Accord- 

 ing as we introduce the different relations of dynamics and thermodynamics, we 

 shall have to examine carefully their possible diagnostic use. 



In statics our work was exclusively of this diagnostic nature. We chose our 

 methods for representing two fields, those of pressure and of mass, and we developed 

 the methods of arriving at these representations, making diagnostic use of two 

 relations, viz, the equation of hydrostatics and the gas-equation, respectively the 

 relation existing between temperature, salinity, pressure, and specific volume of 

 the sea-water. Passing now to kinematics, we shall have to occupy ourselves with 

 the diagnosis of the field of motion. We shall choose methods for representing this 

 field, and try to make complete diagnostic use of all relations of kinematic origin. 



96. The Problem of Prognosis. The present state being diagnosticated, the 

 final problem is that of the precalculation of future states. The solution of this 

 problem will involve the simultaneous use of all intrinsic relations of hydrodynamic 

 and thermodynamic origin, to be used in connection with the initial conditions, the 

 surface conditions, and data regarding exterior effects of terrestrial or cosmic origin. 

 Evidently the problem is of enormous complexity. But in order to try to prepare its 

 solution, we shall solve one by one a series of partial problems belonging to it. For 

 every equation introduced we shall examine its prognostic as well as its diagnostic 

 value. In kinematics we shall meet with the first partial problem of prognosis, for 

 the definition of the fundamental kinematic vectors involves the idea of time. When 

 we know the instantaneous velocity of a moving particle, we shall know the place 

 of this particle a differential of time later. The changes of place of the moving 

 particles can therefore be determined in the first approximation by purely kinematic 

 principles. The solution of this problem of kinematic prognosis is the first step 

 in the solution of the general problem. 



During the work with the problem of prognosis, it will be apparent that while 

 we are probably in possession of all the intrinsic relations to be used for its solution, 

 certain empirical data required for bringing them into application must be sought. 

 The missing data can in many cases be found by reversing the problem of prognosis. 

 The state being known at two epochs, we calculate the missing data, which, used 

 in the intrinsic relations, should allow us to calculate the second state when the 

 first is given. Having this method in view, we shall treat the different partial 

 problems of prognosis both in direct and in inverse form. 



Reversing the problem of kinematic prognosis, we shall thus arrive at the 

 purely kinematic determination of accelerations. When we determine afterwards 

 the same accelerations by dynamic principles, we get the opportunity of finding the 

 value of a term in the dynamic equation, of which we have not a priori a sufficient 

 knowledge, namely, of that representing frictional resistance. 



