2 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



The fields of pressure, of temperature, of humidity, and of salinity are described 

 by the values of the corresponding elements observed in the different points of 

 space. The fields of mass can be described in either of two ways, by the mass per 

 unit volume or by the volume of unit masses. That is, we can consider either 

 density or specific volume as the scalar element describing this field. In the same 

 way we can use two different elements of vector-nature for describing the field of 

 motion, either velocity or specific momentum (Statics, section 3). 



Having defined our variables, we can thus concisely state the problem of 

 meteorology and hydrography : To investigate the five meteorological and the five hydro- 

 graphic elements as functions of coordinates and time. 



88. Investigation of Phenomena Depending upon More Variables. The general 

 principle for investigating phenomena depending upon more variables is this : syste- 

 matically to keep constant a certain variable or group of variables, in order to examine 

 the effect of varying another variable or group of variables. 



We have used this principle in statics already. Independent variables were 

 then only the three coordinates. Among them the two geographical ones evidently 

 form a natural group, having other relations to the investigated fields than the 

 third coordinate, height. This difference determined the method. We began by 

 considering the conditions of equilibrium along certain vertical (or quasi- vertical) 

 lines, namely, the lines along which meteorological ascents or hydrographic soundings 

 had taken place (Statics, Chapters VI and VIII) ; or in mathematical language, 

 we gave to the geographical coordinates the constant values defining the stations 

 and examined the effect of varying the third variable, height. 



Using the results thus obtained, we afterwards drew synoptical charts, repre- 

 senting the fields by horizontal sections instead of by vertical soundings (Statics, 

 Chapters VII and IX). This representation involves a modified use of the same 

 general principle; for a chart shows the effect of varying the two geographical 

 coordinates, while the third independent variable keeps constant. 



When performing investigations according to this general principle it is occasion- 

 ally convenient to let a certain dependent and a certain independent variable change 

 parts. In this way we interchanged pressure and height. Retaining height as the 

 third independent variable, to which the constant values were given, we arrived at 

 isobaric charts drawn in level surfaces (section 65). Using pressure as the third 

 independent variable to which the constant values were given, we arrived at topo- 

 graphic charts of isobaric surfaces (section 64). But in both cases the general 

 result was the same, namely, a representation of the field of pressure in its relation 

 to space, i. e., in reference to coordinates as independent variables. 



Introducing now a fourth independent variable, time, besides the three old ones, 

 the coordinates, we have to apply the same general principle. The first question 

 will then be that of the grouping of the variables. About this question there can be 

 no doubt; for evidently the three coordinates form a natural group, having other 

 relations to the phenomena than the fourth variable, time. The grouping of the 

 variables being agreed upon, we can proceed along two ways: (1) Giving constant 



