78 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



will cut the curves <p= 1,2, 3, . . . of the graphical table, and we can read off those 

 values of /3 or of 7 for which <p has integer values. Then we can set off these points 

 along the curve a = a, on the given chart (fig. 70 b). 



a.=a. t 



B 



Fig. 70. Example of graphical operations with three variables. 



A. Scheme of graphical table. 



B. o, J3, y, given fields. Construction of <p f (a lf 0, y). 



If we construct a graphical table as that of fig. 70 a for each of the curves 

 a = const., we can thus find a complete system of points determining the course of 

 the curves <p = const. 



153. Vector-Algebra. It will be of special importance for us to bring graphi- 

 cal methods into application for mathematical operations concerning vector-fields. 

 It will be useful and save circumlocution when at the same time we introduce a few 

 simple notations of modern vector-analysis.* 



A vector considered as a quantity which has both magnitude and direction will 

 be denoted by a letter in heavy print. The corresponding letter in common print 

 will denote its scalar value or tensor (intensity) . The same letter in common print 

 and with the suffix 5 will denote the projection of the vector on the direction 5. 

 In the same manner we shall by the suffixes x, y, 2 denote the projections on the 

 three rectangular axes x, y, and 2. Thus 



Compare: Gibbs-Wilson, Vector- Analysis, New York, 1901. 



