86 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



of two-dimensional vectors. Tables K in connection with a table for graphical 

 multiplication will thus give the complete solution of the formation of these two 

 products. 



It is easier to explain the graphical procedures by formulae and text than to 

 illustrate them by text-figures, for the text-figures can not be placed upon each other 

 on the illuminated drawing-board in order to make any two systems of curves 

 visible at once as if they were drawn on the same sheet. This should be remembered 

 when studying the example given in fig. 76, which illustrates the formation of the 

 projection of the vector (F, <p) on the direction defined by the angle a. The chart A 



Tables K. Projections of a vector (F, <p). 



represents the field of the given vector (F, <p), the chart B that of the given angle a. 

 The sheets containing these two charts are placed upon each other, and on a third 

 sheet we draw the curves for the difference of angle <p a as illustrated by chart C. 

 We then place the three sheets upon each other in reversed order, taking that which 

 contains the field of a uppermost and draw upon it the curves A = const, illustrated 

 by chart D. On this sheet we have then obtained the chart l which contains the 

 complete result. Thus, while fig. 76 contains five charts, only three sheets of paper 

 have been used. 



157. Addition of Vectors which are Normal to Each Other. In two-dimen- 

 sional vector-algebra the vector-product has lost its character of a proper vector. 

 It can be treated as a scalar, and is therefore easier to form than the vector-sum, 

 which always remains a true vector. In two-dimensional vector-algebra the 

 vector-addition is therefore the only typical vector-operation, and as a rule an 

 operation of more complicated nature than the formation of the products. 



