EXAMPLES OF SOLENOIDAL FIELDS. 43 



(B) Leaving out the lines of equal intensity, and introducing in their place 

 contour-lines giving the relative topography of a second surface of flow over the 

 first, we get the solenoidal representation of the field contained between the two 

 surfaces of flow (fig. 45 b). 



(C) Fig. 45 c gives the horizontal section through the system of unit-tubes. 

 The diagram shows the horizontal projection of the tubes and represents the ver- 

 tical motion by a division of the horizontal plane into areas of equal transport 

 normal to this plane. 



(D) Fig. 45 d gives the lines of flow and the curves of equal intensity for the 

 two-dimensional field contained in a horizontal plane. As in the example in section 

 122 (D), the vertical component A z = az\s independent of x and y and does not 

 therefore require any special representation. But the principle of representing a 

 variable normal component by drawing equiscalar curves is evident at once. 



124. Charts Representing Fields of Motion in Atmosphere and Hydrosphere. 

 Referring to simple examples, we have given four different types of charts for 

 representing fields of motion in space. Each type can be used practically in the 

 case of atmospheric or hydrospheric motions, and we shall later indicate the methods 

 of arriving at each of them. For the purpose of representation each type will have 

 special advantages and special disadvantages. But it would lead too far to develop 

 and exemplify them all in full detail. We shall therefore choose one of the methods 

 as the principal one, namely the method D, i.e., we shall choose arbitrary surfaces 

 cutting through the field, and consider separately the two-dimensional vector-field 

 contained in the surface and the scalar field representing the normal component of 

 the vector. 



As surfaces cutting through the field, we shall use level surfaces, isobaric sur- 

 faces, or for more limited purposes surfaces running parallel to the ground. In order 

 to reduce as much as possible the number of drawings, we shall compose the two- 

 dimensional vector-fields for a series of surfaces. In this manner we shall get two- 

 dimensional vector-fields representing the average tangential motion within sheets 

 of a certain thickness, level sheets, isobaric sheets, or sheets parallel to the ground. 

 We have already made the introductory steps for the determination of such two- 

 dimensional vector-fields from the observations (Chapter II). 



These two-dimensional vector-fields being found as the direct result of the 

 observations, we shall afterwards use the solenoidal condition for deriving the cor- 

 responding scalar fields representing the normal component of motion. It will be 

 most convenient to determine them for the surfaces separating from each other the 

 sheets for which the two-dimensional vector-fields have been drawn. 



The methods for deriving the two-dimensional vector-fields from the observa- 

 tions will be considered in Chapters V-VII. Then Chapters VIII and IX will give 

 from general points of view the graphical methods of perf orming mathematical oper- 

 ations to be used in the subsequent work. These methods being developed, we shall 

 apply them in Chapters X and XI to complete the kinematic diagnosis by deriving 

 the scalar fields which represent the normal component of the motion. 



