84 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



As we count the normal to these surfaces positive upward, the positive rotation 

 around the normal will be a rotation against the motion of the hands of a watch 

 and the positive circulation will be the cyclonic circulation E-N.-W.-S. of the 

 northern hemisphere. (Compare the dial of fig. 32.) 



We shall agree to consider all given angles a, /3, . . . which are used to represent 

 the direction of given vectors as produced by positive rotation from the chosen initial 

 direction. Thus all initially given angles will be represented by positive numbers 

 which are smaller than the number used to represent four right angles, i. e., in our 

 measure positive numbers smaller than 64 (see fig. 75). 



When we form sums or differences of the numbers which represent the given 

 angles we may come both to positive numbers which are greater than 64, and to 

 negative numbers. In such cases we shall always by subtraction or addition of 

 64 (or a multiple of 64) reduce to a positive number smaller than 64. This will 

 always be allowed by the general reason that there is no difference between the 

 direction represented by a and that represented by a four right angles. This 

 remark is of special importance in connection with the difference of angle (8 a, 

 which represents the direction of the vector B relatively to that of A. When we agree 

 always to represent this difference of angle by a positive number, it implies that we 

 agree to count it as produced by a rotation in positive direction from the vector A, of 

 which the anglect a ppears as subtractor to the vector B, of which the angle appears as 

 minuend (see fig. 75). 



These agreements must be remembered for the understanding of our charts, 

 where the isogons, whether they represent absolute angles a, (3 . . .or differences 

 of angle /3 a, are always numbered with positive numbers contained between 

 o and 64. 



Two vectors which cut each other under constant angle will have the same 

 system of isogons, only with different numbers appearing on the isogons. The 

 difference will be zero, if the two vectors have the same direction, 32 if they have the 

 opposite direction, and 16 or 48 if they cut each other under right angle. Evidently 

 two opposite directions will have equal right to be called normal to a given direction. 

 We shall therefore agree to distinguish between these two directions by a rule of 

 signs, namely this : 



From a given direction we pass to that of its positive normal by a rotation of 

 one right angle and to that of its negative normal by a rotation of three right 

 angles in positive direction. 



It follows from this rule that when the vector B is directed along the positive 

 normal to the vector A, the vector A will be directed along the negative normal to 

 the vector B. Or in the notations (a) : The vector 



(B,P) = (B,a+i6) 



is directed along the positive normal to the vector (A, a). But then 



(A, a) = (A, /S-16) = (4, 18+48) 



will be directed along the negative normal to the vector (B,0). 



