CHAPTER I. 



GENERAL CONSIDERATIONS ON THE OBJECT AND THE METHODS OF 

 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



87. The General Problem. Treating statics of atmosphere and of hydrosphere 

 we have considered invariable states of these media. Although passing occasionally 

 the strict limits of statics, we never considered the states from the point of view of 

 their variations, time never entering into our equations. But in entering upon the 

 investigation of these states, not only from the point of view of their distribution 

 in space, but also from that of their variation in time, we have to introduce time as 

 a new independent variable. This allows us to view our problem in its generality 

 and it will be useful to do this before returning to investigations of detail. 



Considering the problem from a mathematical point of view, we have first 

 to define our independent and our dependent variables. 



We consider meteorological and hydrographic phenomena in relation to space 

 and time, *'. e., our independent variables are coordinates and lime. The system of 

 coordinates is always rigidly attached to the earth. Two of the coordinates are the 

 geographical ones, serving to define points at the surface of the land or of the sea; 

 while the third has to give the height above or the depth below sea-level. In our 

 static investigations we have found it convenient to measure this third coordinate 

 in dynamic instead of in geometrical measure, and this will generally be convenient 

 during the continued work. 



As dependent variables we have to introduce the quantities required for defin- 

 ing the state of the atmosphere and the hydrosphere, or formulating the laws of the 

 changes of these states. We shall designate these dependent variables as meteoro- 

 logical or hydrographic elements. The distribution in space of any of these elements 

 is called its field. For the description of atmospheric states we have to consider at 

 least five fields, those of pressure, of mass, of temperature, of humidity, and of 

 motion. The first four of these are scalar fields; the fifth, that of motion, is a 

 vector-field. The question may be raised if the full description of atmospheric 

 states and of the laws of their changes will not require the introduction of still more 

 fields. Thus there may be a mutual dependency upon one another of the meteoro- 

 logical processes and the electric or the magnetic fields of the earth. This would 

 require the introduction of vectors describing these fields as further meteorological 

 elements. But the rational plan will be, first, to treat the problem, as far as possible, 

 with the smallest number of variables. We therefore restrict ourselves to the con- 

 sideration of the five fields already defined for the case of the atmosphere. The five 

 corresponding fields for describing the states of the hydrosphere and for formulating 

 the laws of their changes are the fields of pressure, of mass, of temperature, of 

 salinity, and of motion, precisely the same as in the case of the atmosphere, except 

 that salinity takes the place of humidity. 



