6 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



The kinetic energy per unit-mass has the cUmensions of the square of a velocity 

 [Z 2 Z~ 2 ]. The kinetic energy per unit-volume is the square of the velocity multi- 

 plied by the density of the moving medium [J/Z _1 Z -2 ]. The units of each of 

 these quantities in the m.t.s. system are equal to 10,000 of their c.g.s. units. They 

 are perfectly equivalent to each other for the description of the field of kinetic 

 energy in a moving medium. The work per unit-mass and per unit-volume have 

 the same dimensions, respectively, as the kinetic energy per unit-mass and per unit- 

 volume, and can be measured by the same units. 



Activities referred either to unit-mass or to unit-volume come into considera- 

 tion when processes of continuous transformations of energy are going on in the 

 medium. The units of these quantities in the m.t.s. system are also equal to 

 10,000 of the corresponding c.g.s. units. 



The gravity potential is a quantity which has the character of a work per unit- 

 mass [Z 2 Z -2 ], while a pressure is a quantity which has the character of a work 

 per unit-volume [iJ/Z _1 Z _2 ]. The pressure is defined in a more elementary 

 manner as a force per unit-area. But, however the definition be chosen, potential 

 and pressure are closely related to each other from a theoretical point of view, and 

 in a broader sense of the word they may be considered as corresponding quantities. 

 Their dimensions differ by a quantity of the dimensions of a density, and their units 

 in the m.t.s. s) y stem are equal to 10,000 of their c.g.s. units. As the units of these 

 two quantities are of special importance to us, the)' will be discussed separately. 



4. Units of Gravity Potential. To every point in space we attribute a certain 

 value of the gravity potential, defined numerically by this rule: It is equal to the 

 potential energy relatively to sea-level possessed by a unit-mass situated in the 

 point. The gravity potential of a point is therefore equal to the amount of work 

 required to lift unit-mass from sea-level to the point against the action of gravity. 



To unit-increase of gravity potential will therefore correspond, in any given 

 locality, a definite increase of height, numerically equal to the reciprocal value of 

 the acceleration of gravity. This increase of height will be slightly different in dif- 

 ferent localities, depending on the variations from place to place of the acceleration 

 of gravity. But setting smaller variations aside, and taking 10 for the acceleration of 

 gravity in the m.t.s. system, the height giving unit rise of potential will be equal to 

 a decimeter. 



To fix in our minds the approximate value of this height, we shall call the m.t.s. 

 unit of gravity potential a dynamic decimeter. A ten times greater unit is the 

 dynamic meter. Expressing gravity potentials in this latter unit, we gain the prac- 

 tical advantage that the number giving the gravity potential of a point will be very 

 nearly equal to the number giving its height above or its depth below sea-level, 

 expressed in common meters. This fortunate accordance makes it very convenient 

 to use the dynamic meter as a technical unit of gravity potential. Values of the 

 gravity potential expressed by an integer number of dynamic meters will be called 

 standard values, and will be used very much as representatives tor heights or 

 depths. 



