CHAPTER III. 



ELEMENTARY PRINCIPLES OF KINEMATICS OF CONTINUOUS MEDIA. 



109. Kinematics of a Continuous Medium. We have considered the observa- 

 tions from which we shall derive our diagnosis of atmospheric or hydrospheric states 

 of motion. We shall then proceed to develop the general principles of kinematics 

 which shall govern the diagnostic work. 



In order to arrive at these general principles, we shall consider atmosphere, 

 hydrosphere, and solid earth as a material system which fills space continuously. 

 We shall neglect phenomena related to the molecular structure of these bodies, 

 such as the diffusion of water-vapor through air or of salt through water. In the 

 same manner we shall neglect every transfer of mass from one of these bodies to 

 any other of them. Thus we shall set out of consideration the transfer of mass 

 from the sea or from the moist ground to the air by the evaporation of water, and 

 the return of these masses to the sea or to the porous ground in the form of rain. 

 These processes will be of high importance in connection with the thermodynamics 

 of atmosphere and hydrosphere. But from the pure kinematic point of view they 

 will be insignificant, as they will give mass-transports which are small compared 

 with those connected with the great air-motions or sea-motions. 



It will therefore be sufficient for our present purpose to consider a material 

 medium which fills space continuously. Density or specific volume may vary from 

 particle to particle of the medium, even in discontinuous manner, as at the surface 

 of separation between air and sea. The dynamic properties are not taken into 

 consideration. The only condition to be observed is that of the material nature 

 of the medium, involving the principle that every moving particle shall have an invari- 

 able mass, together with the supplementary condition that the medium shall fill space 

 continuously. 



To describe the instantaneous state of motion of this medium we shall use two 

 vectors, velocity and specific momentum. The conditions of the material nature of 

 the medium, and of its continuity in space, do not restrict the generality of the 

 fields of these vectors. The methods of representing them geometrically will there- 

 fore be the methods of representing geometrically a vector-field of unlimited 

 generality. From a formal point of view this chapter will therefore deal with the 

 subject of the geometrical representation of vector-fields, and will thus contain 

 results which we shall use later in connection with other vectors. 



While the conditions of the material nature of the medium and of its continuity 

 in space do not restrict the geometrical properties of the field of motion, they will 



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