io8 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



(see fig. 87). This principle for dividing the curve C into elements has the advan- 

 tage that it at once leads to the determination of the bands of unit transport in the 

 cases where the vector is solenoidal. 



The vector-bands being chosen, we know that the transport T is given by the 

 product 



(b) T = A dn 



A being the intensity of the vector and dn the breadth of the band. In order to find 

 the field of the scalar T, we have first to form the field of the line-element dn. This 

 is done by making continuous use of the divided sheet for direct length-measurements 



0.5 OJt 0.3 



Fig. 87. 



A. Vector curves 5 (with arrow-heads) and intensity curves A = 10, 9, 8, 7, . . . (fine continuous lines). 



B. Vector curves s (with arrow-heads) and curves of equal transport T= 1.1, 1.0,0.9, (fine continuous lines). 



(fig. 86). The curves n along which the line-elements dn should be measured need 

 not be drawn; for the sheet can with the same ease be placed with its ordinates 

 normal to as parallel to the given curves s. Afterwards the graphical multiplication 

 of the field of dn by that of the intensity A gives the field of transport T, correspond- 

 ing to the vector-bands. When the elements of the initial curve C fulfil the con- 

 dition (a) this curve will appear as the curve T = i in the field of transport. 



That the use described of the divided sheet is a process of differentiation from 

 the analytical point of view is thus seen : The choice of vector-lines by the division 

 of the initial curve C into elements corresponds to the choice of a continuous scalar 

 function a which has these vector-lines for equiscalar curves 01=1,2,3, . . . T 

 will then be expressed by the equation : 



(&') T = A^ 



da 



where d a = 1 for the chosen interval between the successive curves. 



