7 6 



DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



Tables J. Graphical division. 



II. Dividend tabulated as function of quotient 

 and divisor. 



151. Division of Scalar Fields. Now 



let / (a, /3) = " . We shall then have to 



a 



0' 



construct the field of the scalar <p, which is 

 the ratio of the two scalars a and /3, 



(a) f> = j 



We here meet with the case that the 

 function <p is asymmetric with respect to 

 the two variables. Solving with respect 

 to each of them we get 



(b) 





or 



a = P (p 



Fig. 69. Graphical division. The fine lines = 2,3,4, 

 . . . represent the dividend; the fine line /3 = 1 2, 11, 

 10,9,. . .the divisor; the thick lines < = 1.1, 1.0,0.9, 

 . . . the quotient. 



These equations lead to the two tables J. 

 The first of them is the same as that serving 

 graphical multiplication (table I), though 

 other values of the arguments appear to 

 suit the example of fig. 69. The second is 

 an ordinary multiplication-table. 



The first of tables J shows for instance that the curve <p = o.6 is to be drawn 

 through that point of the curve a = 5 where |8 = 8.3, through that point of the curve 

 a = 4 where /? = 6.7, through that point of the curve a = 3, where /3 = 5.0, and so on. 

 The second table J shows in the same manner that the curve <p = 0.6 is to be drawn 

 through that point of the curve = 9 where = 5.4, through that point of the curve 

 j8 = 8 where a = 4.8, and so on. Observing thus the tabulated numbers, we can draw 

 continuously one by one the curves <p = const., which represent the required field. 



