68 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



When the charts are drawn on semi-transparent paper, no special device is 

 required to color the tooth- wheel or the chisel. A coloring paper can be placed 

 under the transparent sheet upon which the isogonal curves are drawn. The line- 

 elements will then come on the under-side of the sheet, but will be seen through it. 



When an instrument like one of these is at hand, it will be found very con- 

 venient to draw the lines of flow in the indirect way, using the isogons as auxiliary 

 curves. Of course the indirect method will always require more time than the 

 direct one. The latter will therefore be preferable for rapid work. But the indirect 

 method gives a much higher degree of precision, and should therefore be preferred 

 when the purpose is quantitative scientific investigations. 



144. Equivalence of Isogons and Vector-Lines for the Representation of Vector- 

 Fields. We have introduced the isogons as auxiliary curves for tracing the vector- 

 lines ; but in reality they are perfectly equivalent to these lines for the representation 

 of the field. We shall therefore have henceforth to reckon with two different repre- 

 sentations of the vector-fields ; by intensity-curves in connection with vector-lines, 

 and by intensity-curves in connection with isogons. We have used the first con- 

 sistently hitherto because it gives the most conspicuous picture. But our work 

 will consist henceforth in the performance of mathematical operations upon the field, 

 and these operations are in many cases performed more easily when the direction of 

 the vector is given by the isogons. Therefore, in the following chapters, when we 

 are going to study methods for performing elementary algebraic or infinitesimal 

 operations upon the fields, we shall have to take into consideration the one method 

 of representing the vector as well as the other, trying to utilize the special advantages 

 of each of them. 



