CHAPTER V. 



DIRECT DRAWING OF THE LINES OF FLOW AND THE CURVES OF EQUAL 

 INTENSITY FOR THE TWO-DIMENSIONAL VECTOR-FIELDS. 



125. Continuous Representation of the Two-Dimensional Vector- Fields. 

 Passing to the practical diagnostic work, our first problem will be this: From 

 the observations of motion (local values or averages for certain sheets) to draw 

 the lines of flow and the curves of equal intensity for the corresponding two-dimen- 

 sional field. Drawing these curves we shall get a continuous representation of this 

 field instead of the discontinuous representation given by the observations them- 

 selves.* 



Our solutions of concrete problems of this kind are given on plates XXXII, 

 XXXVIII, LV, and LVII b to LX b. The lines of flow are represented by heavy 

 curves provided with arrow-heads, the curves of equal intensity by thinner curves. 



As such continuous representations of the two-dimensional fields are to form 

 the basis for every further step in kinematic diagnosis or prognosis, we can not dis- 

 cuss too carefully the methods for drawing them as correctly as possible. Referring 

 to the mentioned plates as examples, we shall take up this discussion, which will 

 occupy us in this as well as in the two following chapters. 



126. Equiscalar Curves in the Field of Single-Valued Scalar Quantities. The 



numbers representing the numerical value of the vectors velocity or specific momen- 

 tum define a scalar field having the same geometrical features as the well-known 

 fields of other scalars, like pressure or temperature. The method of drawing the 

 curves of equal intensity of a vector is therefore precisely the same as that of drawing 

 isothermal or isobaric curves ; but as the curves in the case before us will have an 

 irregular course, the drawing will require a good deal of care. 



Equiscalar curves are never drawn exclusively by the use of the numbers repre- 

 senting the observations. Otherwise an infinite number of observations would be 

 required for the determination of their course. The intrinsic properties of the 

 scalar quantity are also taken into consideration. The main property used in draw- 

 ing the common synoptical charts is this, that the scalar is single-valued. As it can 

 never have two different values in one point, two different curves, representing differ- 

 ent values of the scalar, can never intersect each other. This property gives to the field 

 of the single-valued scalar features which are totally different from those of the 

 multiple-valued scalar, which we shall have to consider later. 



*That charts of this character have not yet been used in practical meteorology, must be on account of their 

 apparent complexity. The only charts containing lines of flow of atmospheric motions which we have been able to 

 find in literature have been drawn by Rene de Saussure (Archives des Sciences Physiques et Naturelles, Quatrieme 

 Periode, T, 5, p. 497, Geneve, 1898) and by Jean Bertrand (Bulletin de la Societe beige d'Astronomie et de Meteorologie, 

 1905, No. 7 and 8; see also Physikalische Zeitschrift, 1905, p. 853). 



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